Tesis sobre el tema "Quantum many body"
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1
Bausch, Johannes Karl Richard. "Quantum stochastic processes and quantum many-body physics". Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/269857.
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This dissertation investigates the theory of quantum stochastic processes and its applications in quantum many-body physics. The main goal is to analyse complexity-theoretic aspects of both static and dynamic properties of physical systems modelled by quantum stochastic processes. The thesis consists of two parts: the first one addresses the computational complexity of certain quantum and classical divisibility questions, whereas the second one addresses the topic of Hamiltonian complexity theory. In the divisibility part, we discuss the question whether one can efficiently sub-divide a map describing the evolution of a system in a noisy environment, i.e. a CPTP- or stochastic map for quantum and classical processes, respectively, and we prove that taking the nth root of a CPTP or stochastic map is an NP-complete problem. Furthermore, we show that answering the question whether one can divide up a random variable $X$ into a sum of $n$ iid random variables $Y_i$, i.e. $X=\sum_{i=1}^n Y_i$, is poly-time computable; relaxing the iid condition renders the problem NP-hard. In the local Hamiltonian part, we study computation embedded into the ground state of a many-body quantum system, going beyond "history state" constructions with a linear clock. We first develop a series of mathematical techniques which allow us to study the energy spectrum of the resulting Hamiltonian, and extend classical string rewriting to the quantum setting. This allows us to construct the most physically-realistic QMAEXP-complete instances for the LOCAL HAMILTONIAN problem (i.e. the question of estimating the ground state energy of a quantum many-body system) known to date, both in one- and three dimensions. Furthermore, we study weighted versions of linear history state constructions, allowing us to obtain tight lower and upper bounds on the promise gap of the LOCAL HAMILTONIAN problem in various cases. We finally study a classical embedding of a Busy Beaver Turing Machine into a low-dimensional lattice spin model, which allows us to dictate a transition from a purely classical phase to a Toric Code phase at arbitrarily large and potentially even uncomputable system sizes.
2
Riera, Graells Arnau. "Entanglement in Many Body Quantum Systems". Doctoral thesis, Universitat de Barcelona, 2010. http://hdl.handle.net/10803/1600.
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THESIS SUMMARYTEXT:
This thesis is made of two parts. In the first one, the issue of entanglement in many body systems is addressed. The concept of entanglement and some of the recent progress on the study of entropy of entanglement in many body quantum systems are reviewed. Emphasis is placed on the scaling properties of entropy for one-dimensional models at quantum phase transitions.
Then, we focus on the area-law scaling of the entanglement entropy. An explicit computation in arbitrary dimensions of the entanglement entropy of the ground state of a discretized scalar free field theory that shows the expected area law result is also presented. For this system, it is shown that area law scaling is a manifestation of a deeper reordering of the vacuum produced by majorization relations.
To finish this first part, the issue of how simple can a quantum system be such as to give a highly entangled ground state is addressed. In particular, we propose a Hamiltonian of a XX model with a ground state whose entropy scales linearly with the size of the block. It provides a simple example of a one dimensional system of spin-1/2 particles with nearest neighbour interactions that violates area-law for the entanglement entropy.
The second part of this thesis deals with the problem of simulating quantum mechanics for highly entangled systems. Two different approaches to this issue are considered. One consists of using ultra-cold atoms systems as quantum simulators. With this aim, some experimental techniques related to cold atoms that allow to simulate strongly correlated many body quantum systems are reviewed an explicit example of simulation is presented. In particular, we analyze how to achieve a Mott state of Laughlin wave functions in an optical lattice and study the consequences of considering anharmonic corrections to each single site potential expansion that were not taken into account until now.
Finally, a different approach to simulate strongly correlated systems is considered: to use small quantum computers to simulate them. An explicit quantum algorithm that creates the Laughlin state for an arbitrary number of particles n in the case of falling fraction equal to one is presented. We further prove the optimality of the circuit using permutation theory arguments and we compute exactly how entanglement develops along the action of each gate. We also discuss its experimental feasibility decomposing the qudits and the gates in terms of qubits and two qubit-gates as well as the generalization to arbitrary falling fraction.
KEYWORDS: Entanglement, Many body quantum systems, Quantum Information Condensed Matter, Cold atoms, Spin chains, Quantum simulator, Quantum computation.
"Entrellaçament quàntic en sistemes de molts cossos"
TEXT:
Aquesta tesi està composada per dues parts. En la primera, adrecem la qüestió de l'entrellaçament quàntic en els sistemes de molts cossos. Així, introduïm primer el concepte d'entrellaçament i revisem els progressos recents sobre aquest camp. A continuació, ens centrem la llei d'àrea per l'entropia d'entrellaçament i presentem un càlcul explícit d'aquesta entropia per a l'estat fonamental d'un camp escalar no interactuant obtenint la llei d'àrea esperada. Finalment, acabem aquesta part presentant un sistema molt senzill 1-dimensional que tot i tenir interaccions locals mostra una llei de volum per l'entropia.
En la segona part de la tesi tractem el problema de la simulació de sistemes quàntics altament entrellaçats. Considerem dos possibles vies per tractar aquest problema. Una d'elles consisteix en la utilització d'àtoms ultra-freds com a simuladors quàntics. En particular, analitzem un mètode per obtenir un estat producte de funcions d'ona de Laughlin en un xarxa òptica i estudiem les conseqüències de considerar la correcció anharmònica de l'expansió del potencial a cada pou de la xarxa. Finalment, considerem una altra aproximació a la simulació de sistemes fortament correlacionats: utilitzar petits ordinadors quàntics per a simular-los. Per il.lustrar aquest tipus de simulació, presentem un algoritme quàntic que crea un estat de Laughlin per un nombre arbitrari de partícules i en el cas de fracció d'ocupació 1.
3
Graham, Abi Claire. "Many-body interactions in quantum wires". Thesis, University of Cambridge, 2004. https://www.repository.cam.ac.uk/handle/1810/284031.
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The first part of this thesis describes transport measurements of long quantum wires, which are affected by disorder. The resulting additional features in the conductance are characterised, and the results are discussed in the context of the Luttinger liquid model. Realistic strategies for controlling disorder in long wires are suggested, which should eliminate many of the problems associated with experimental studies of Luttinger liquids. Disorder effects are further investigated using a new lithography technique called Erasable Electrostatic Lithography (EEL). A scanning probe tip at a fixed voltage is used to locally charge surface states above a long disordered quantum wire. This allows the potential of the disordered wire to be manipulated, with the creation of microconstrictions and quasi-bound states inside the wire. The importance of electron-electron interactions in short 1D systems was demonstrated in 1996 by the discovery of the 0.7 structure. This is an additional quasi-plateau in the conductance at a value of around 0.7(2e2/h) and is a universal phenomenon in quantum wires. The main result of this thesis is the discovery of non-quantised conductance structures at the crossings of spin-split 1D subbands which have similar characteristics to the 0.7 structure. We call these new structures 0.7 analogues. It is shown that the 0.7 analogue is accompanied by a spontaneous splitting and abrupt restructuring of energy levels in the region of the crossing, which is thought to be an exchange effect. We believe that this gives valuable new insight into the origin of the 0.7 structure.
4
Jia, Ningyuan. "Quantum Many-Body Physics with Photons". Thesis, The University of Chicago, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10928150.
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Understanding and manipulating quantum materials is a long-sought goal in both the condensed matter and cold atom communities. Photons have recently emerged as a good candidate for studying quantum many-body states due to their fast dynamics and convenient manipulation. Tremendous efforts have been made to engineer single particle Hamiltonian with non-trivial topology. Having individual photons to strongly collide with each other and form an entangled many-body state remained as a challenge in optical domain.
In this thesis, I will first demonstrate how to engineer artificial magnetic field and non-trivial topology for microwave photons. In a classical lumped element circuit, we demonstrate the edge modes for microwave photons within the bulk band, and also show that these modes propagates with topological protection against the local lattice disorder. This work paves the way to synthesize correlated quantum materials in a lattice using microwave photons, combined with circuit QED technique.
Recently, Rydberg-Rydberg interaction has been broadly used in cold atom experiment to generate long-range inter-particle coupling for quantum information processing and quantum material simulation. We combine this technique with cavity electromagnetically induced transparency and create a robust quasi-particle, cavity Rydberg polaritons, which harness the power from both cavity photons with exotic topology and Rydberg atoms with strong interactions. We first demonstrate the interaction in the single quanta level in a quantum dot with single cavity mode and further expand it into multi-mode regime with modulated atomic states.
5
Scarlatella, Orazio. "Driven-Dissipative Quantum Many-Body Systems". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS281/document.
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Ma thèse de doctorat était consacrée à l'étude des systèmes quantiques à plusieurs corps dissipatifs et pilotés. Ces systèmes représentent des plateformes naturelles pour explorer des questions fondamentales sur la matière dans des conditions de non-équilibre, tout en ayant un impact potentiel sur les technologies quantiques émergentes. Dans cette thèse, nous discutons d'une décomposition spectrale de fonctions de Green de systèmes ouverts markoviens, que nous appliquons à un modèle d'oscillateur quantique de van der Pol. Nous soulignons qu’une propriété de signe des fonctions spectrales des systèmes d’équilibre ne s’imposait pas dans le cas de systèmes ouverts, ce qui produisait une surprenante "densité d’états négative", avec des conséquences physiques directes. Nous étudions ensuite la transition de phase entre une phase normale et une phase superfluide dans un système prototype de bosons dissipatifs forcés sur un réseau. Cette transition est caractérisée par une criticité à fréquence finie correspondant à la rupture spontanée de l'invariance par translation dans le temps, qui n’a pas d’analogue dans des systèmes à l’équilibre. Nous discutons le diagramme de phase en champ moyen d'une phase isolante de Mott stabilisée par dissipation, potentiellement pertinente pour des expériences en cours. Nos résultats suggèrent qu'il existe un compromis entre la fidélité de la phase stationnaire à un isolant de Mott et la robustesse d'une telle phase à taux de saut fini. Enfin, nous présentons des développements concernant la théorie du champ moyen dynamique (DMFT) pour l’étude des systèmes à plusieurs corps dissipatifs et forcés. Nous introduisons DMFT dans le contexte des modèles dissipatifs et forcés et nous développons une méthode pour résoudre le problème auxiliaire d'une impureté couplée simultanément à un environnement markovien et à un environnement non-markovien. À titre de test, nous appliquons cette nouvelle méthode à un modèle simple d’impureté fermioniqueMy PhD was devoted to the study of driven-dissipative quantum many-body systems. These systems represent natural platforms to explore fundamental questions about matter under non-equilibrium conditions, having at the same time a potential impact on emerging quantum technologies. In this thesis, we discuss a spectral decomposition of single-particle Green functions of Markovian open systems, that we applied to a model of a quantum van der Pol oscillator. We point out that a sign property of spectral functions of equilibrium systems doesn't hold in the case of open systems, resulting in a surprising ``negative density of states", with direct physical consequences. We study the phase transition between a normal and a superfluid phase in a prototype system of driven-dissipative bosons on a lattice. This transition is characterized by a finite-frequency criticality corresponding to the spontaneous break of time-translational invariance, which has no analog in equilibrium systems. Later, we discuss the mean-field phase diagram of a Mott insulating phase stabilized by dissipation, which is potentially relevant for ongoing experiments. Our results suggest that there is a trade off between the fidelity of the stationary phase to a Mott insulator and robustness of such a phase at finite hopping. Finally, we present some developments towards using dynamical mean field theory (DMFT) for studying driven-dissipative lattice systems. We introduce DMFT in the context of driven-dissipative models and developed a method to solve the auxiliary problem of a single impurity, coupled simultaneously to a Markovian and a non-Markovian environment. As a test, we applied this novel method to a simple model of a fermionic, single-mode impurity
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Wesslén, Carl-Johan. "Many-Body effects in Semiconductor Nanostructures". Licentiate thesis, Stockholms universitet, Fysikum, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-102344.
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Low dimensional semiconductor structures are modeled using techniques from the field of many-body atomic physics. B-splines are used to create a one-particle basis, used to solve the more complex many-body problems. Details on methods such as the Configuration Interaction (CI), Many-Body Perturbation Theory (MBPT) and Coupled Cluster (CC) are discussed. Results from the CC singles and doubles method are compared to other high-precision methods for the circular harmonic oscillator quantum dot. The results show a good agreement for the energy of many-body states of up to 12 electrons. Properties of elliptical quantum dots, circular quantum dots, quantum rings and concentric quantum rings are all reviewed. The effects of tilted external magnetic fields applied to the elliptical dot are discussed, and the energy splitting between the lowest singlet and triplet states is explored for varying geometrical properties. Results are compared to experimental energy splittings for the same system containing 2 electrons.
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Mur, Petit Jordi. "Many-body studies on atomic quantum systems". Doctoral thesis, Universitat de Barcelona, 2006. http://hdl.handle.net/10803/1587.
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En aquesta tesi presentem un conjunt d'estudis sobre sistemes atòmics on els efectes quàntics són especialment destacats. Aquests estudis s'han dut a terme aplicant diverses tècniques de la física teòrica de molts cossos.En primer lloc hem estudiat la possible existència d'una transició de fase superfluida en un gas ultrafred d'àtoms fermiònics, mitjançant una generalització de la teoria BCS de la superconductivitat que dóna especial rellevància al paper jugat per l'asimetria de densitat entre les dues espècies, i permet que l'estat fonamental presenti un trencament espontani de simetria.
En una segona part, hem estudiat la dinàmica d'un condensat de Bose-Einstein el grau de llibertat d'espí del qual pot evolucionar dins d'una trampa òptica quasi-unidimensional, tant a temperatura zero com finita, mitjançant una formulació de camp mitjà.
Finalment, hem dut a terme un estudi detallat de l'estat fonamental i la tensió lineal de sistemes bidimensional d'heli-4, primerament mitjançant les tècniques de Monte Carlo, i posteriorment amb un funcional de la densitat construit amb aquest objectiu.
EN CASTELLÀ:
En esta tesis se presenta un conjunto de estudios sobre sistemas atómicos donde los efectos cuánticos son especialmente destacados. Dichos estudios se han llevado a cabo aplicando varias técnicas de la física teórica de muchos cuerpos.
En primer lugar, se ha estudiado la posible existencia de una transición superfluida en un gas ultrafrío de átomos fermiónicos mediante una generalización de la teoría BCS de la superconductividad que presta especial atención al papel jugado por la asimetría de densidad entre las dos especies, y permite que el estado fundamental presente una rotura espontánea de simetría.
En una segunda parte, se ha estudiado la dinámica de un condensado de Bose-Einstein cuyo grado de libertad de espín puede evolucionar en una trampa óptica cuasi-unidimensional, tanto a temperatura cero como finita, mediante una formulación de campo medio.
Finalmente, se ha llevado a cabo un estudio detallado del estado fundamental y la tensión lineal de sistemas bidimensionales de helio-4, primeramente mediante las técnicas de Monte Carlo, y posteriormente con un funcional de la densidad construido al efecto.
PALABRAS CLAVE: Átomos fríos, Aparejamiento, Condensado espinorial, Helio, Dos dimensiones
SUMMARY:
This thesis presents a set of studies on atomic systems where quantum efects are particularly relevant. These studies have been developed by applying a variety of tools from many-body physics.
First of all, we have studied the prospects for the existance of a superfluid transition in an ultracold gas of fermionic atoms, by generalizing the BCS theory of superconductivity to the case when the two species that pair have different densities and the ground state may spontaneously break one or more symmetries.
In a second part, we have studied the dynamics of a Bose-Einstein condensate whose spin degree of freedom is free to evolve inside a quasi-onedimensional optical trap. We have used a mean-field formulation to address both the zero temperature case and the finite temperature one.
Finally, we have performed a careful study of the ground state and the line tension of two-dimensional systems of helium-4. First, we have used Monte Carlo techniques, then with a Density Functional built on-purpose.
KEYWORDS: Cold gases, Pairing, Spinor condensate, Helium, Two dimensions
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Heyl, Markus Philip Ludwig. "Nonequilibrium phenomena in many-body quantum systems". Diss., lmu, 2012. http://nbn-resolving.de/urn:nbn:de:bvb:19-145838.
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Young, Carolyn 1979. "Many-body cotunneling in coupled quantum dots". Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101692.
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The zero-temperature equilibrium conductance of mesoscopic devices due to single-particle resonant tunneling was first described by Landauer [1]. The Landauer formula was later extended to the multi-channel case by Fisher and Lee [2], who reduced the problem of calculating electronic transport properties to the problem of solving for the Green's function for a given system geometry.In this work, the single-particle formalism is extended to the study of higher-order two-particle cotunneling processes by considering many-body Green's functions. The effect of attaching leads to the system is described in terms of a two-particle self-energy, whose analytical form is written in terms of a Feynman path integral over all possible tunneling processes between the leads and the device. In addition, an efficient numerical technique for the calculation of the fully dressed Green's function of a device region attached to two-particle leads is presented.
The problem of two-particle transport is then approached, and an analogy to single-particle transport on the infinite plane is drawn. It is shown that, for nonspin flip cotunneling processes, the two-particle transport result can be related to the single-particle conductance by way of a simple convolution. Finally, results for the cotunneling contribution to the conductance of double quantum dots, or charge qubits, are presented.
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Brell, Courtney Gordon Gray. "Many-body models for topological quantum information". Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/13539.
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We develop and investigate several quantum many-body spin models of use for topological quantum information processing and storage. These models fall into two categories: those that are designed to be more realistic than alternative models with similar phenomenology, and those that are designed to have richer phenomenology than related models. In the first category, we present a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the perturbative low-energy limits of entirely two-body Hamiltonians. This construction reproduces the target models' behavior using only couplings which are natural in terms of the original Hamiltonians. As an extension of this work, we construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). We define a perturbative Hamiltonian with a finite order low energy effective Hamiltonian that is a gapped, frustration-free parent Hamiltonian for an encoded version of a desired PEPS. For topologically ordered PEPS, the ground space of the low energy effective Hamiltonian is shown to be in the same phase as the desired state to all orders of perturbation theory. We then move on to define models that generalize the phenomenology of several well-known systems. We first define generalized cluster states based on finite group algebras, and investigate properties of these states including their PEPS representations, global symmetries, relationship to the Kitaev quantum double models, and possible applications. Finally, we propose a generalization of the color codes based on finite groups. For non-Abelian groups, the resulting model supports non-Abelian anyonic quasiparticles and topological order. We examine the properties of these models such as their relationship to Kitaev quantum double models, quasiparticle spectrum, and boundary structure.
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Costa, De Almeida Ricardo. "Entanglement certification in quantum many-body systems". Doctoral thesis, Università degli studi di Trento, 2022. https://hdl.handle.net/11572/356801.
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Entanglement is a fundamental property of quantum systems and its characterization is a central problem for physics. Moreover, there is an increasing demand for scalable protocols that can certify the presence of entanglement. This is primarily due to the role of entanglement as a crucial resource for quantum technologies. However, systematic entanglement certification is highly challenging, and this is particularly the case for quantum many-body systems. In this dissertation, we tackle this challenge and introduce some techniques that allow the certification of multipartite entanglement in many-body systems. This is demonstrated with an application to a model of interacting fermions that shows the presence of resilient multipartite entanglement at finite temperatures. Moreover, we also discuss some subtleties concerning the definition entanglement in systems of indistinguishable particles and provide a formal characterization of multipartite mode entanglement. This requires us to work with an abstract formalism that can be used to define entanglement in quantum many-body systems without reference to a specific structure of the states. To further showcase this technique, and also motivated by current quantum simulation efforts, we use it to extend the framework of entanglement witnesses to lattice gauge theories.L'entanglement è una proprietà fondamentale dei sistemi quantistici e la sua caratterizzazione è un problema centrale per la fisica. Inoltre, vi è una crescente richiesta di protocolli scalabili in grado di certificare la presenza di entanglement. Ciò è dovuto principalmente al ruolo dell'entanglement come risorsa cruciale per le tecnologie quantistiche. Tuttavia, la certificazione sistematica dell'entanglement è molto impegnativa, e questo è particolarmente vero per i sistemi quantistici a molti corpi. In questa dissertazione, affrontiamo questa sfida e introduciamo alcune tecniche che consentono la certificazione dell'entanglement multipartito in sistemi a molti corpi. Ciò è dimostrato con un'applicazione a un modello di fermioni interagenti che mostra la presenza di entanglement multipartito resiliente a temperature finite. Inoltre, discutiamo anche alcune sottigliezze riguardanti la definizione di entanglement in sistemi di particelle indistinguibili e forniamo una caratterizzazione formale dell'entanglement multipartito. Ciò ci richiede di lavorare con un formalismo astratto che può essere utilizzato per definire l'entanglement nei sistemi quantistici a molti corpi senza fare riferimento a una struttura specifica degli stati. Per mostrare ulteriormente questa tecnica, e anche motivata dagli attuali sforzi di simulazione quantistica, la usiamo per estendere la struttura dei testimoni di entanglement alle teorie di gauge del reticolo.
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Biella, Alberto. "Many-body physics in open quantum systems". Doctoral thesis, Scuola Normale Superiore, 2016. http://hdl.handle.net/11384/85905.
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Tomadin, Andrea. "Dynamical instabilities in quantum many-body systems". Doctoral thesis, Scuola Normale Superiore, 2010. http://hdl.handle.net/11384/85874.
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from the introduction: "[...] This thesis addresses the problem of the nonequilibrium time-evolution of
many-body sistems realized with quantum simulators. We investigate theoretically
the relation between the time-evolution and the equilibrium phase diagram
in the presence of a quantum phase transition. The long-time evolution of the
systems is investigated, both in the case of conservative dynamics and under the
action of dissipative processes.
The thesis is organized as follows. Chaps. 1-3 contain theoretical and experimental
facts that are relevant to the present work. In the Chap. 1 we describe the
quantum simulator realized with fermionic cold atoms in the bulk of an optical
trap. In the Chap. 2 we describe the microresonators where light and matter are
strongly coupled, and we focus on the implementation of a quantum simulator
with defect-cavities in photonic crystals. In Chap. 3 several theoretical works
concerning the nonequilibrium dynamics of many-body systems are summarized.
Chaps. 4{6 contain the original contributions of this thesis. In Chap. 4 we investigate
the time-evolution of an ensemble of fermionic atoms after an abrupt
change of the interaction strength from a vanishing to a weak attractive value. In
Chap. 5 we demonstrate the possibility to measure the quantum phase transition
between a super fluid and a Mott-insulator state in an array of microresonators, in
the presence of the leakage of photons out of the cavities. In Chap. 6 we study a
system of cold bosonic atoms coupled to a tailored bath that dissipatively drives
the system into a super fluid or into a thermal state.
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Mertens, Christopher J. "Many-body theory of dissipative quantum optical systems". Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/30316.
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Turro, Francesco. "Quantum algorithms for many-body structure and dynamics". Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/345459.
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Nuclei are objects made of nucleons, protons and neutrons. Several dynamical processes that occur in nuclei are of great interest for the scientific community and for possible applications. For example, nuclear fusion can help us produce a large amount of energy with a limited use of resources and environmental impact. Few-nucleon scattering is an essential ingredient to understand and describe the physics of the core of a star. The classical computational algorithms that aim to simulate microscopic quantum systems suffer from the exponential growth of the computational time when the number of particles is increased. Even using today's most powerful HPC devices, the simulation of many processes, such as the nuclear scattering and fusion, is out of reach due to the excessive amount of computational time needed. In the 1980s, Feynman suggested that quantum computers might be more efficient than classical devices in simulating many-particle quantum systems. Following Feynman's idea of quantum computing, a complete change in the computation devices and in the simulation protocols has been explored in the recent years, moving towards quantum computations. Recently, the perspective of a realistic implementation of efficient quantum calculations was proved both experimentally and theoretically. Nevertheless, we are not in an era of fully functional quantum devices yet, but rather in the so-called "Noisy Intermediate-Scale Quantum" (NISQ) era. As of today, quantum simulations still suffer from the limitations of imperfect gate implementations and the quantum noise of the machine that impair the performance of the device. In this NISQ era, studies of complex nuclear systems are out of reach. The evolution and improvement of quantum devices will hopefully help us solve hard quantum problems in the coming years. At present quantum machines can be used to produce demonstrations or, at best, preliminary studies of the dynamics of a few nucleons systems (or other equivalent simple quantum systems). These systems are to be considered mostly toy models for developing prospective quantum algorithms. However, in the future, these algorithms may become efficient enough to allow simulating complex quantum systems in a quantum device, proving more efficient than classical devices, and eventually helping us study hard quantum systems. This is the main goal of this work, developing quantum algorithms, potentially useful in studying the quantum many body problem, and attempting to implement such quantum algorithms in different, existing quantum devices. In particular, the simulations made use of the IBM QPU's , of the Advanced Quantum Testbed (AQT) at Lawrence Berkeley National Laboratory (LBNL), and of the quantum testbed recently based at Lawrence Livermore National Laboratory (LLNL) (or using a device-level simulator of this machine). The our research aims are to develop quantum algorithms for general quantum processors. Therefore, the same developed quantum algorithms are implemented in different quantum processors to test their efficiency. Moreover, some uses of quantum processors are also conditioned by their availability during the time span of my PhD.
The most common way to implement some quantum algorithms is to combine a discrete set of so-called elementary gates. A quantum operation is then realized in term of a sequence of such gates. This approach suffers from the large number of gates (depth of a quantum circuit) generally needed to describe the dynamics of a complex system. An excessively large circuit depth is problematic, since the presence of quantum noise would effectively erase all the information during the simulation. It is still possible to use error-correction techniques, but they require a huge amount of extra quantum register (ancilla qubits). An alternative technique that can be used to address these problems is the so-called "optimal control technique". Specifically, rather than employing a set of pre-packaged quantum gates, it is possible to optimize the external physical drive (for example, a suitably modulated electromagnetic pulse) that encodes a multi-level complex quantum gate. In this thesis, we start from the work of Holland et al. "Optimal control for the quantum simulation of nuclear dynamics" Physical Review A 101.6 (2020): 062307, where a quantum simulation of real-time neutron-neutron dynamics is proposed, in which the propagation of the system is enacted by a single dense multi-level gate derived from the nuclear spin-interaction at leading order (LO) of chiral effective field theory (EFT) through an optimal control technique.
Hence, we will generalize the two neutron spin simulations, re-including spatial degrees of freedom with a hybrid algorithm. The spin dynamics are implemented within the quantum processor and the spatial dynamics are computed applying classical algorithms. We called this method classical-quantum coprocessing. The quantum simulations using optimized optimal control methods and discrete get set approach will be presented. By applying the coprocessing scheme through the optimal control, we have a possible bottleneck due to the requested classical computational time to compute the microwave pulses. A solution to this problem will be presented. Furthermore, an investigation of an improved way to efficiently compile quantum circuits based on the Similarity Renormalization Group will be discussed. This method simplifies the compilation in terms of digital gates. The most important result contained in this thesis is the development of an algorithm for performing an imaginary time propagation on a quantum chip. It belongs to the class of methods for evaluating the ground state of a quantum system, based on operating a Wick rotation of the real time evolution operator. The resulting propagator is not unitary, implementing in some way a dissipation mechanism that naturally leads the system towards its lowest energy state. Evolution in imaginary time is a well-known technique for finding the ground state of quantum many-body systems. It is at the heart of several numerical methods, including Quantum Monte Carlo techniques, that have been used with great success in quantum chemistry, condensed matter and nuclear physics. The classical implementations of imaginary time propagation suffer (with few exceptions) of an exponential increase in the computational cost with the dimension of the system. This fact calls for a generalization of the algorithm to quantum computers. The proposed algorithm is implemented by expanding the Hilbert space of the system under investigation by means of ancillary qubits. The projection is obtained by applying a series of unitary transformations having the effect of dissipating the components of the initial state along excited states of the Hamiltonian into the ancillary space. A measurement of the ancillary qubit(s) will then remove such components, effectively implementing a "cooling" of the system. The theory and testing of this method, along with some proposals for improvements will be thoroughly discussed in the dedicated chapter.
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Elliott, Thomas Joseph. "Topics in quantum measurement of many-body systems". Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:c3c792c8-c184-41a3-abfc-868f5965a852.
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In quantum physics, measurement exhibits fundamentally different behaviour to the classical case, having direct effect on the observed system. As a result, the very act of observation in quantum systems plays a non-trivial role, and can be used as a method of controlling the dynamics of the system. With the rise of quantum technologies, understanding and exploiting these phenomena offers a great boon. Here, we investigate a selection of the possibilities offered by quantum measurement for characterising and manipulating many-body systems, with particular focus on ultracold atomic gases. We first study how microscopic quantum structures can be used to indirectly probe larger systems. After deriving a general result, we consider the specific case of impurity atoms immersed in a quantum gas, and demonstrate that this enables density-related properties of the gas to be inferred from measurements of solely the impurity internal state. Following this, we explore how the backaction from measurement can be used for control of quantum systems. Utilising the quantum Zeno effect that results from persistent measurement of a quantum state, we show how fully-quantum many-body light-matter interactions enable the engineering of atomic states and dynamics through measurement of the light, leading to an abundance of interesting phenomena, including genuinely multipartite entangled states, long-range correlated tunnelling, and the quantum simulation of long-range and correlated interactions. The resulting structure imparted by the light on the matter can also be used to detect and measure atomic entanglement. Finally, we generalise quantum Zeno dynamics to the regime where the measurement timestep is finite, and demonstrate that the resulting system evolution can exhibit correlated processes.
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Yoshida, Beni. "Studying many-body physics through quantum coding theory". Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/77257.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (p. 133-140).
The emerging closeness between correlated spin systems and error-correcting codes enables us to use coding theoretical techniques to study physical properties of many-body spin systems. This thesis illustrates the use of classical and quantum coding theory in classifying quantum phases arising in many-body spin systems via a systematic study of stabilizer Hamiltonians with translation symmetries. In the first part, we ask what kinds of quantum phases may arise in gapped spin systems on a D-dimensional lattice. We address this condensed matter theoretical question by giving a complete classification of quantum phases arising in stabilizer Hamiltonians at fixed points of RG transformations for D = 1; 2; 3. We found a certain dimensional duality on geometric shapes of logical operators where m-dimensional and (D m)-dimensional logical operators always form anti-commuting pairs (m is an integer). We demonstrate that quantum phases are completely classified by topological characterizations of logical operators where topological quantum phase transitions are driven by non-analytical changes of geometric shapes of logical operators. As a consequence, we argue that topological order is unstable at any nonzero temperature and self-correcting quantum memory in a strict sense may not exist where the memory time is upper bounded by some constant at a fixed temperature, regardless of the system size. Our result also implies that topological field theory is the universal theory for stabilizer Hamiltonians with continuous scale symmetries. In the second part, we ask the fundamental limit on information storage capacity of discrete spin systems. There is a well-known theoretical limit on the amount of information that can be reliably stored in a given volume of discrete spin systems. Yet, previously known systems were far below this theoretical limit. We propose a construction of classical stabilizer Hamiltonians which asymptotically saturate this limit. Our model borrows an idea from fractal geometries arising in the Sierpinski triangle, and is a rare manifestation of limit cycle behaviors with discrete scale symmetries in real-space RG transformations, which may be beyond descriptions of topological field theory.
by Beni Yoshida.
Ph.D.
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Alkurtass, B. "A quantum information approach to many-body problems". Thesis, University College London (University of London), 2015. http://discovery.ucl.ac.uk/1469005/.
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This thesis investigates the properties of entanglement in one-dimensional many-body systems. In the first part, the non-equilibrium dynamics following a sudden global quench are exploited for the purpose of generating long-range entanglement. A number of initial states are considered. It is shown that the dynamics following the considered quench can be mapped to the problem of a state transfer. The quench can then be optimised by exploiting the literature about quantum state transfer to generate maximal long-range entanglement and maximal block entropy. In the second part of the thesis, a spin chain emulation of the two-channel, Kondo (2CK) model is proposed. Studying the local magnetisation and susceptibility we show that the spin-only emulation truly represent the two-channel Kondo model and extract the Kondo temperature. A detailed entanglement analysis is presented. Using density matrix renormalisation group (DMRG), which allow for real space analysis, Kondo temperature and Kondo length are evaluated. An entanglement measure, namely the negativity, as well as the Schmidt gap are used as possible order parameters predicting the critical point. An extensive analysis of the block entropy of the system is presented for different limiting values of Kondo coupling. A universal scaling of the impurity contribution to the entropy is found and the 2CK residual entropy is extracted. The last part explores quench dynamics in Kondo systems using time-dependent DMRG. For a quench in the Kondo coupling a travelling and breathing clouds are ob-served. A measurement-induced dynamics lead to an oscillation between an effective singlet and triplet states of the impurity and the Kondo cloud. Kondo temperature can be extracted from the frequency of the oscillation.
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Fusco, Lorenzo. "Non-equilibrium thermodynamics in quantum many-body systems". Thesis, Queen's University Belfast, 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706680.
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Thermodynamics is one of the pillars of modern science. Understanding which are the boundaries for the applicability of a theory is fundamental for every science and thermodynamics makes no exception. This Thesis studied the implications of thermodynamic transformations applied to quantum systems, particularly discussing the limits of a proper thermodynamic interpretation of such a transformation for a quantum many-body system. First a framework is developed to give a physical meaning to the full statistics of the work distributions for a many-body system, with particular emphasis on the quantum Ising model. Signatures of criticality are found at any level of the statistics of the work distribution. Furthermore, a detailed study of cyclic work extraction protocols is reported, for the case of the Dicke model, analysing the interplay between entanglement and phase transition from the point of view of non-equilibrium thermodynamics. Afterwards, a study of non-equilibrium thermodynamics of open quantum systems is reported. The first experimental reconstruction of the irreversible entropy production for a critical quantum manybody system is demonstrated, showing an excellent agreement with the theoretical predictions. Finally, in the framework of thermodynamics of quantum jump trajectories, a novel approach to the resolution of the large-deviation function is derived. Using this method many studies on the thermodynamics of open quantum many-body systems can be realised in the future.
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Henriet, Loïc. "Non-equilibrium dynamics of many body quantum systems". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX036/document.
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Cette thèse porte sur l'étude de propriétés dynamiques de modèles quantiques portés hors équilibre. Nous introduisons en particulier des modèles généraux de type spin-boson, qui décrivent par exemple l'interaction lumière-matière ou certains phénomènes de dissipation. Nous contribuons au développement d'une approche stochastique exacte permettant de d'écrire la dynamique hors équilibre du spin dans ces modèles. Dans ce contexte, l'effet de l'environnement bosonique est pris en compte par l'intermédiaire des degrés de liberté stochastiques supplémentaires, dont les corrélations temporelles dépendent des propriétés spectrales de l'environnement bosonique. Nous appliquons cette approche à l'étude de phénomènes à N-corps, comme par exemple la transition de phase dissipative induite par un environnement bosonique de type ohmique. Des phénomènes de synchronisation spontanée, et de transition de phase topologique sont aussi identifiés. Des progrès sont aussi réalisés dans l'étude de la dynamique dans les réseaux de systèmes lumière-matière couplés. Ces développements théoriques sont motivés par les progrès expérimentaux récents, qui permettent d'envisager une étude approfondie de ces phénomènes. Cela inclut notamment les systèmes d'atomes ultra-froids, d'ions piégés, et les plateformes d'électrodynamique en cavité et en circuit. Nous intéressons aussi à la physique des systèmes hybrides comprenant des dispositifs à points quantiques mésoscopiques couplés à un résonateur électromagnétique. L'avènement de ces systèmes permet de mesures de la formation d'états à N-corps de type Kondo grâce au résonateur; et d'envisager des dispositifs thermoélectriquesThis thesis deals with the study of dynamical properties of out-of-equilibrium quantum systems. We introduce in particular a general class of Spin-Boson models, which describe for example light-matter interaction or dissipative phenomena. We contribute to the development of a stochastic approach to describe the spin dynamics in these models. In this context, the effect of the bosonic environment is encapsulated into additional stochastic degrees of freedom whose time-correlations are determined by spectral properties of the bosonic environment. We use this approach to study many-body phenomena such as the dissipative quantum phase transition induced by an ohmic bosonic environment. Synchronization phenomena as well as dissipative topological transitions are identified. We also progress in the study of arrays of interacting light-matter systems. These theoretical developments follow recent experimental achievements, which could ensure a quantitative study of these phenomena. This notably includes ultra-cold atoms, trapped ions and cavity and circuit electrodynamics setups. We also investigate hybrid systems comprising electronic quantum dots coupled to electromagnetic resonators, which enable us to provide a spectroscopic analysis of many-body phenomena linked to the Kondo effect. We also introducethermoelectric applications in these devices
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Rotondo, P. "EMERGENT COLLECTIVE PHENOMENA IN QUANTUM MANY-BODY SYSTEMS". Doctoral thesis, Università degli Studi di Milano, 2016. http://hdl.handle.net/2434/361054.
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Motivated by a recent proposal by Lev and coworkers, in the first part of this thesis, we will perform a theoretical investigation of a new class of quantum simulators: the so called multimode disordered Dicke simulators.
Our approach is mostly inspired from Statistical Mechanics: indeed we will merge together exact results obtained in the context of the Dicke model by Hepp and Lieb, with known results on disordered systems and neural networks. In this way we will be able to generalize the standard approach to the superradiant phase transition to the disordered case. As a byproduct of this analysis we will argue that this new class of quantum simulators (properly engineered) may be an alternative (or complementary) route toward quantum computation.
Also the second part of the thesis has a ”quantum simulators motivation”. Recently Bloch’s group implemented an Ising quantum magnet with long-range antiferro- magnetic interactions, which exhibits a peculiar devil’s staircase phase diagram, predicted long ago by Bak and Bruinsma.
This result, joined with recent theoretical investigations by Lesanowsky and coworkers suggested to us to reconsider these spin models in the context of the fractional quantum Hall effect (FQHE).
In the second part of this thesis we will show that the quantum Hall Hamitonian projected on the lowest Landau level can be mapped, in the so called thin torus limit, on the lattice gas studied by Bak and Bruinsma. This observation will lead us to predict a devil’s staircase scenario for the Hall conductance as a function of the magnetic field. This work stimulated us to investigate the connection between Laughlin wave function and Tao-Thouless states, that we will explore in the last section of the second part.
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Hernández, Santana Senaida. "Local temperature and correlations in quantum many-body systems". Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/666722.
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Quantum Mechanics was established as the theory of the microscopic world, which allowed to understand processes in atoms and molecules. Its emergence led to a new scientific paradigm that quickly spread to different research fields. Two relevant examples are Quantum Thermodynamics and Quantum Many-Body Theory, where the former aims to characterize thermodynamic processes in quantum systems and the latter intends to understand the properties of quantum many-body systems. In this thesis, we tackle some of the questions in the overlap between these disciplines, focusing on the concepts of temperature and correlations. Specifically, it contains results on the following topics: locality of temperature, correlations in long-range interacting systems and thermometry at low temperature. The problem of locality of temperature is considered for a system at thermal equilibrium and consists in studying whether it is possible to assign a temperature to any of the subsystems of the global system such that both local and global temperatures are equal. We tackle this problem in two different settings, for generic one-dimensional spin chains and for a bosonic system with a phase transition at non-zero temperature. In the first case, we consider generic one-dimensional translation-invariant spin systems with short-range interactions and prove that it is always possible to assign a local temperature equal to the global one for any temperature, including at criticality. For the second case, we consider a three-dimensional discretized version of the Bose-Einstein model at the grand canonical ensemble for some temperature and particle density, and characterize its non-zero-temperature phase transition. Then, we show that temperature is locally well-defined at any temperature and at any particle density, including at the phase transition. Additionally, we observe a qualitative relation between correlations and locality of temperature in the system. Moving to correlations, we consider fermionic two-site long-range interacting systems at thermal equilibrium. We show that correlations between anti-commutative operators at non-zero temperature are upper bounded by a function that decays polynomially with the distance and with an exponent that is equal to the interaction exponent, which characterizes the interactions in the Hamiltonian. Moreover, we show that our bound is asymptotically tight and that the results extend to density-density correlations as well as other types of correlations for quadratic and fermionic Hamiltonians with long-range interactions. Regarding the results on thermometry, we consider a bosonic model and prove that strong coupling between the probe and the system can boost the thermal sensitivity for low temperature. Furthermore, we provide a feasible measurement scheme capable of producing optimal estimates at the considered regime.La Mecánica Cuántica fue establecida como la teoría del mundo microscópico, el cual permitió entender los procesos en átomos y moléculas. Su nacimiento llevo a un nuevo paradigma científico que se propagó rápidamente a otros campos de investigación. Dos ejemplos relevantes son la Termodinámica Cuántica y la Teoría Cuántica de muchos cuerpos, donde la primera pretende caracterizar los procesos termodinamicos en sistemas cuántico y la segunda intenta entender las propiedades de los sistemas cuánticos de muchos cuerpos. En esta tesis, atacamos algunas de las preguntas en la intersección entre estas disciplinas, enfocandonos en los conceptos de la temperatura y las correlaciones. Específicamente, contiene resutlados en os siguientes temas: localidad de la temperature, correlaciones en sistemas interactuantes de largo alcance y termometría a baja temperature. El problema de localidad de la temperatura es considerado para un sistema a equilibrio térmico y consiste en estudiar si es posible asignar temperature a cualquiera de los subsistemas del sistema global tal que la temperature local y global sean equivalentes. Atacamos este problemas en dos casos diferentes, for cadenas de spines genéricas y para un sistema de bosones con una transición de fase a temperature distinta a cero. En el primer caso, consideramos sistemas de espines invarantes traslacional y de una dimensión con interactions de corto alcance y provamos que siempre es posible asignar una temperature local igual a la global para cualquier temperature, incluyendo en la criticalidad. Para el segundo caso, consideramos una versión 3D y discretizada del modelo de Bose-Einstein en el estado gran canónico para alguna temperature y densidad de partículas, y caracterizamos su transición a temperatura distinta a cero. Luego, mostramos que la temperature esta localmente bien definida a cualquier temperature y cualquier densidad de partículas, incluyendo en la transición de fase. Adicionalment, observamos una relación cualitativa entre las correlaciones y la localidad de la temperature en el sistema. Moviéndonos a las correlaciones, consideramos sistemas fermiónicos de con interaction entre dos cuerpos y de largo alcance a equilibrio térmico. Mostramos que las correlations entre los operadores anti-comutativos at temperatura distinta a cero estan acotadas por arriba por una función que decae polinomiamente con la distancia y con un exponent que es igual al exponente de interacción, el cual caracteriza las interacciones en el Hamiltoniano. Además, mostrado que nuestro límite es "ajustado" asintoticamente y que los resultados se extiense a correlations entre operadores de densidad y a otros tipos de correlaciones para Hamiltonianos cuadráticos y fermiónicos con interacciones de largo alcance. Sobre los resultados en termometría, consideramos un modelo bosónico y provamos que el acoplamiento fuerte entre el termómetro y el sistema pueda incrementar la sensibilidad térmica para baja temperatura. Además, explicamos un esquema de medida accesible y capaz de producir estimación óptimas en el régimen que consideramos
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Hallnäs, Martin. "Exactly solved quantum many-body systems in one dimension". Licentiate thesis, KTH, Physics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-564.
Texto completoResumen
This thesis is devoted to the study of various examples of exactly solved quantum many-body systems in one-dimension. It is divided into two parts: the ¯rst provides background and complementary results to the second, which consists of three scienti¯c papers. The ¯rst paper concerns a particu- lar extension, corresponding to the root system CN, of the delta-interaction model. We prove by construction that its exact solution, even in the gen- eral case of distinguishable particles, can be obtained by the coordinate Bethe ansatz. We also elaborate on the physical interpretation of this model. It is well known that the delta-interaction is included in a four parameter family of local interactions. In the second paper we interpret these parameters as cou- pling constants of certain momentum dependent interactions and determine all cases leading to a many-body system of distinguishable particles which can be solved by the coordinate Bethe ansatz. In the third paper we consider the so-called rational Calogero-Sutherland model, describing an arbitrary number of particles on the real line, con¯ned by a harmonic oscillator potential and interacting via a two-body interaction proportional to the inverse square of the inter-particle distance. We construct a novel solution algorithm for this model which enables us to obtain explicit formulas for its eigenfunctions. We also show that our algorithm applies, with minor changes, to all extensions of the rational Calogero-Sutherland model which correspond to a classical root system.
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Hallnäs, Martin. "Quantum many-body systems exactly solved by special functions". Doctoral thesis, KTH, Teoretisk fysik, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4416.
Texto completoResumen
This thesis concerns two types of quantum many-body systems in one dimension exactly solved by special functions: firstly, systems with interactions localised at points and solved by the (coordinate) Bethe ansatz; secondly, systems of Calogero-Sutherland type, as well as certain recently introduced deformations thereof, with eigenfunctions given by natural many-variable generalisations of classical (orthogonal) polynomials. The thesis is divided into two parts. The first provides background and a few complementary results, while the second presents the main results of this thesis in five appended scientific papers. In the first paper we consider two complementary quantum many-body systems with local interactions related to the root systems CN, one with delta-interactions, and the other with certain momentum dependent interactions commonly known as delta-prime interactions. We prove, by construction, that the former is exactly solvable by the Bethe ansatz in the general case of distinguishable particles, and that the latter is similarly solvable only in the case of bosons or fermions. We also establish a simple strong/weak coupling duality between the two models and elaborate on their physical interpretations. In the second paper we consider a well-known four-parameter family of local interactions in one dimension. In particular, we determine all such interactions leading to a quantum many-body system of distinguishable particles exactly solvable by the Bethe ansatz. We find that there are two families of such systems: the first is described by a one-parameter deformation of the delta-interaction model, while the second features a particular one-parameter combination of the delta and the delta-prime interactions. In papers 3-5 we construct and study particular series representations for the eigenfunctions of a family of Calogero-Sutherland models naturally associated with the classical (orthogonal) polynomials. In our construction, the eigenfunctions are given by linear combinations of certain symmetric polynomials generalising the so-called Schur polynomials, with explicit and rather simple coefficients. In paper 5 we also generalise certain of these results to the so-called deformed Calogero-Sutherland operators.QC 20100712
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Biamonte, Jacob Daniel. "Categorical models of quantum information in many-body systems". Thesis, University of Oxford, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.540124.
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Hallnäs, Martin. "Quantum many-body systems exactly solved by special functions /". Stockholm : Department of Theoretical Physics, Royal Institute of Technology, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4416.
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Jones, Andrew. "Quantum drude oscillators for accurate many-body intermolecular forces". Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4878.
Texto completoResumen
One of the important early applications of Quantum Mechanics was to explain the Van-der-Waal’s 1/R6 potential that is observed experimentally between two neutral species, such as noble gas atoms, in terms of correlated uncertainty between interacting dipoles, an effect that does not occur in the classical limit [London-Eisenschitz,1930]. When many-body correlations and higher-multipole interactions are taken into account they yield additional many-body and higher-multipole dispersion terms. Dispersion energies are closely related to electrostatic interactions and polarisation [Hirschfelder-Curtiss-Bird,1954]. Hydrogen bonding, the dominant force in water, is an example of an electrostatic effect, which is also strongly modified by polarisation effects. The behaviour of ions is also strongly influenced by polarisation. Where hydrogen bonding is disrupted, dispersion tends to act as a more constant cohesive force. It is the only attractive force that exists between hydrophobes, for example. Thus all three are important for understanding the detailed behaviour of water, and effects that happen in water, such as the solvation of ions, hydrophobic de-wetting, and thus biological nano-structures. Current molecular simulation methods rarely go beyond pair-wise potentials, and so lose the rich detail of many-body polarisation and dispersion that would permit a force field to be transferable between different environments. Empirical force-fields fitted in the gas phase, which is dominated by two-body interactions, generally do not perform well in the condensed (many-body) phases. The leading omitted dispersion term is the Axilrod-Teller-Muto 3-body potential, which does not feature in standard biophysical force-fields. Polarization is also usually ommitted, but it is sometimes included in next-generation force-fields following seminal work by Cochran [1971]. In practice, many-body forces are approximated using two-body potentials fitted to reflect bulk behaviour, but these are not transferable because they do not reproduce detailed behaviour well, resulting in spurious results near inhomogeneities, such as solvated hydrophobes and ions, surfaces and interfaces. The Quantum Drude Oscillator model (QDO) unifies many-body, multipole polarisation and dispersion, intrinsically treating them on an equal footing, potentially leading to simpler, more accurate, and more transferable force fields when it is applied in molecular simulations. The Drude Oscillator is simply a model atom wherein a single pseudoelectron is bound harmonically to a single pseudonucleus, that interacts via damped coulomb interactions [Drude,1900]. Path Integral [Feynman-Hibbs,1965] Molecular Dynamics (PIMD) can, in principle, provide an exact treatment for moving molecules at finite temperature on the Born- Oppenheimer surface due to their pseudo-electrons. PIMD can be applied to large systems, as it scales like N log(N), with multiplicative prefactor P that can be effectively parallelized away on modern supercomputers. There are other ways to treat dispersion, but all are computationally intensive and cannot be applied to large systems. These include, for example, Density Functional Theory provides an existence proof that a functional exists to include dispersion, but we dont know the functional. We outline the existing methods, and then present new density matrices to improve the discretisation of the path integral. Diffusion Monte Carlo (DMC), first proposed by Fermi, allows the fast computation of high-accuracy energies for static nuclear configurations, making it a useful method for model development, such as fitting repulsion potentials, but there is no straightforward way to generate forces. We derived new methods and trial wavefunctions for DMC, allowing the computation of energies for much larger systems to high accuracy. A Quantum Drude model of Xenon, fit in the gas-phase, was simulated in the condensed-phase using both DMC and PIMD. The new DMC methods allowed for calculation of the bulk modulus and lattice constant of FCC-solid Xenon. Both were in excellent agreement with experiment even though this model was fitted in the gasphase, demonstrating the power of Quantum Drudes to build transferable models by capturing many-body effects. We also used the Xenon model to test the new PIMD methods. Finally, we present the outline of a new QDO model of water, including QDO parameters fitted to the polarisabilities and dispersion coefficients of water.
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Nandkishore, Rahul (Rahul Mahajan ). "Quantum many body physics in single and bilayer graphene". Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/79522.
Texto completoResumen
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.Cataloged from PDF version of thesis.
Includes bibliographical references.
Two dimensional electron systems (2DES) provide a uniquely promising avenue for investigation of many body physics. Graphene constitutes a new and unusual 2DES, which may give rise to unexpected collective phenomena. However, the vanishing density of states in charge neutral single layer graphene suppresses many body effects, and one has to alter the system to observe strongly ordered states. We consider three ways of accessing quantum many body physics using graphene. First, we consider doping single layer graphene to a Van Hove singularity in the density of states. We show that there are strong instabilities to several strongly ordered states, with the leading instability being to a d-wave superconducting state. The superconducting state realizes chiral superconductivity, an exotic form of superconductivity wherein the phase of the order parameter winds by 4[pi] as we go around the Fermi surface. We also discuss the nature of the spin density wave state which is the principal competitor to superconductivity in doped graphene. Next, we study bilayer graphene (BLG), which has a non-vanishing density of states even at charge neutrality. We show that Coulomb interactions give rise to a zero bias anomaly in the tunneling density of states for BLG, which manifests itself at high energy scales. We also show that the quadratic band crossing in BLG is unstable to arbitrarily weak interactions, and estimate the energy scale for formation of strongly ordered states. We show that gapped states in BLG have topological properties, and we classify the various possible gapped and gapless states in terms of symmetries. We study the competition between various ordered states, and discuss how the nature of the ground state may be deduced experimentally. We also discuss recent experimental observations of strongly ordered states in bilayer graphene. Finally, we study bilayer graphene in a transverse magnetic field, focusing on the properties of the quantum Hall ferromagnet (QHF) state. We resolve an apparent discrepancy between the experimentally observed energetics and theory. We close with a discussion of the exotic topological defects that form above the QHF state.
by Rahul Nandkishore.
Ph.D.
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Sengupta, Sanghita. "Quantum Many - Body Interaction Effects In Two - Dimensional Materials". ScholarWorks @ UVM, 2018. https://scholarworks.uvm.edu/graddis/939.
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In this talk, I will discuss three problems related to the novel physics of two-dimensional quantum materials such as graphene, group-VI dichalcogenides family (TMDCs viz. MoS2 , WS2, MoSe2 , etc) and Silicene-Germanene class of materials.
The first problem poses a simple question - how do the quantum excitations in a graphene membrane affect adsorption? Using the tools of diagrammatic perturbation theory, I will derive the scattering rates of a neutral atom on a graphene membrane. I will show how this seemingly naive model can serve as a non-relativistic condensed matter analogue of the infamous infrared problem in Quantum Electrodynamics.
In the second problem, I will move from the framework of a single atom adsorption to a collective behavior of fluids near graphene and TMDC - interfaces. Following the seminal work of Dzyaloshinskii-Lifshitz-Pitaevskii on van der Waals interactions, I will develop a theory of liquid film growth on 2 dimensional surfaces. Additionally, I will report an exotic phenomenon of critical wetting instability which is a result of the dielectric engineering and discuss experimental and technological implications.
Finally, the last problem will see the introduction of spin-orbit coupling effects in the 2D topological insulator family of Silicene-Germanene class of materials. I will present a unified theory for their in-plane magnetic field response leading to "anomalous", i.e electron interaction-dependent spin-flip transition moment. Can this correction to spin-flip transition moment be measured? I will propose magneto-optical experimental techniques that can probe the effects.
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Ros, Valentina. "Aspects of localization in disordered many-body quantum systems". Doctoral thesis, SISSA, 2016. http://hdl.handle.net/20.500.11767/4906.
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For a quantum system to be permanently out-of-equilibrium, some non-trivial mechanism must be at play, to counteract the general tendency of entropy increase and flow toward equilibration. Among the possible ways to protect a system against local thermalization, the phenomenon of localization induced by quenched disorder appears to be one of the most promising. Although the problem of localization was introduced almost sixty years ago, its many-body version is still partly unresolved, despite the recent theoretical effort to
tackle it. In this thesis we address a few aspects of the localized phase, mainly focusing on the interacting case. A large part of the thesis is devoted to investigating the underlying “integrable” structure of many-body localized systems, i.e., the existence of non-trivial conservation laws that prevent ergodicity and thermalization. In particular, we show that such conserved operators can be explicitly constructed by dressing perturbatively the non-interacting conserved quantities, in a procedure that converges when scattering processes are weak enough. This is reminiscent of the quasiparticle theory in Fermi liquids, although in the disordered case the construction extends to the full many-body energy spectrum, and it results in operators that are exactly conserved. As an example of how to use the constructive recipe for the conserved quantities, we compute the long-time limit of an order parameter for the MBL phase in antiferromagnetic spin systems. Similar analytical tools as the ones exploited for the construction of the conserved operators are then applied to the problem of the stability of single-particle localization with respect to the coupling to a finite bath. In this context, we identify a quantum-Zeno-type effect, whereby the bath unexpectedly enhances the particle’s localization. In the final part of the thesis, we discuss several mechanisms by which thermal fluctuations may influence the spatial localization of excitations in interacting many-body states.
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Keck, Maximilian. "Many-body open quantum systems: from dynamics to thermodynamics". Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85919.
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This thesis studies problems concerning the dynamics and thermodynamics of manybody
quantum systems. We start by introducing the necessary theoretical concepts and
tools forming the basis of this manuscript. The research presented can be split in two
parts. The first one deals with the dynamics of many-body quantum systems subject to
environmental dissipative effects of various forms, while the second one studies topics
of thermodynamics in many-body quantum systems.
The first part of the research presented studies the effects of an environment inducing
dissipation. We establish and study the adiabatic dynamics of free-fermion models
subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian.
The merit of these models is that they can be solved exactly, which thus can help us
to study the interplay between non-adiabatic transitions and dissipation in many-body
quantum systems. After the adiabatic evolution, we evaluate the excess energy (average
value of the Hamiltonian) as a measure of the deviation from reaching the target
final ground state. We find a robust evidence of the fact that an optimal working time
for the quantum annealing protocol emerges as a result of the competition between the
non-adiabatic effects and the dissipative processes. We compare these results with matrix
product operator simulations of an Ising system and show that the phenomenology
we found applies also for this more realistic case.
We then proceed to a scenario in which the environment is not detrimental, but is
on the contrary the driving force of the effects studied. We demonstrate that persistent
currents can be induced in a quantum system in contact with a structured reservoir,
without the need of any applied gauge field. The working principle of the mechanism
leading to their presence is based on the extension to the many-body scenario of
non-reciprocal Lindblad dynamics. Specifically, we consider an interacting spin/boson
model in a ring-shaped one-dimensional lattice coupled to an external bath. By employing
a combination of cluster mean-field, exact diagonalization and matrix product
operator techniques, we show that solely dissipative effects suffice to engineer steady
states with a persistent current that survives in the limit of large systems. We also
verify the robustness of such current in the presence of additional dissipative or Hamiltonian
perturbation terms.
The second part studies many-body quantum systems with a focus on thermodynamics.
First, we investigate a quantum battery made of N two-level systems, which
is charged by an optical mode via an energy-conserving interaction. We quantify the
fraction of energy stored in the battery that can be extracted in order to perform
thermodynamic work. We first demonstrate that this fraction is highly reduced by the presence of correlations between the charger and the battery or between the two-level
systems composing the battery. We then show that the correlation-induced suppression
of extractable energy, however, can be mitigated by preparing the charger in a
coherent optical state. We conclude by proving that the charger-battery system is
asymptotically free of such locking correlations in the N ! 1 limit.
And lastly, we study open questions within the theory of open quantum systems.
The Markovian evolution of an open quantum system is characterized by a positive
entropy production, while the global entropy gets redistributed between the system
and the environmental degrees of freedom. Starting from these premises, we analyse
the entropy variation of an open quantum system in terms of two distinct relations:
the Clausius inequality, that provides an intrinsic bound for the entropy variation in
terms of the heat absorbed by the system, and an extrinsic inequality, which instead
relates the former to the corresponding entropy increment of the environment. By
modeling the thermalization process with a Markovian collisional model, we compare
and discuss the two bounds, showing that the latter is asymptotically saturated in the
limit of large interaction time. In this regime not only the reduced density matrix
of the system reaches an equilibrium configuration, but it also factorizes from the
environmental degrees of freedom.
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Beconcini, Michael. "Quantum transport and many-body effects in encapsulated graphene". Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85922.
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Unlike any other material, graphene is all surface. This means that it is
strongly affected by its surroundings, including the substrate it lays upon.
In the past few years, it was understood that silicon oxide (SiO2), the most
popular substrate material for graphene, limits the performance of graphene
devices and obscures interesting physics. Hexagonal boron nitride (hBN)
has emerged as “the perfect” substrate that results in graphene devices of
astonishing electronic quality. In this Thesis, we explore some peculiar nonlocal
effects that are found in such new devices due to quantum transport
and electron-electron interactions in the coherent as well as the diffusive
regime. Chapters 1-4 are devoted to the introduction of some basic concepts
and to the main experimental facts that motivated our work.
Since encapsulation in hBN crystals makes graphene practically insusceptible
to the environment, electrons can travel micrometer distances without
scattering. In Chapter 5, in the framework of the Landauer-Büttiker scattering
theory, we have developed a scaling procedure for numerical simulations
of tight-binding nonlocal transport in realistic graphene devices. We
have tested our method against experimental data on transverse magnetic
focusing (TMF). This comparison enables a clear physical interpretation of
all the observed features of the TMF signal, including its oscillating sign.
Moreover, in graphene/hBN superlattices and in bilayer graphene in a
perpendicular electric field, which have broken inversion symmetry, topological
currents originating from graphene’s two valleys flow in opposite
directions and combine to produce long-range charge neutral flow. This effect
translates into a nonlocal voltage at zero magnetic fields in a narrow
energy range near Dirac points at distances as large as several micrometers.
However, the behavior of the observed long-range nonlocality as a function
of temperature, band gap, and carrier concentration remained to be understood.
In Chapter 6 and 7, we have showen, using a diffusive theory, that
this behavior can be explained with bulk topological transport and Coulomb
drag between the electrons belonging to the two different valleys, in good
agreement with experimental findings.
Finally, in Chapter 8, we have studied the crossed Andreev reflection in
a three-terminal hybrid graphene/superconductor system in the quantum
Hall regime and its effect on the nonlocal resistances.
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Marzolino, Ugo. "Entanglement and decoherence in many-body physics". Doctoral thesis, Università degli studi di Trieste, 2011. http://hdl.handle.net/10077/5827.
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2009/2010The thesis deals with several features of quantum many-body systems. They are described both in terms of reversible unitary transformations and as an environment interacting with other systems. An introductory part introduces the main ideas of quantum noise and dissipative dynamics. A chapter is also dedicated to some useful aspects of entanglement. The second part of the thesis concerns the orginal results. A chapter describes the dynamics of two qubits interacting with a common environment. This chapter is focused on the derivation of a new Markovian approximation, finer than the standard weak coupling limit, and its application on the dynamical generation of the entanglement. The second topic concerns the developping of some procedures to reconstruct the parameters governing a large class of Markovian and non-Markovian dissipative dynamics of a quantum particle. These procedures are based on the symplectic tomography of the evolved state. The third topic concerns the physics of many identical bosons, with a special focus on Bose-Einstein condensates. The relevance of entanglement and spin squeezing for quantum metrology with high accuracy is discussed in connection with the quantum Fisher information and collective and squeezing inequalities. A third part summerizes the results. Some useful tools are described in the appendices.
XXIII Ciclo
1983
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Shi, Bowen. "Anyon theory in gapped many-body systems from entanglement". The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587705058308889.
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Benedikter, Niels [Verfasser]. "Effective Evolution Equations from Many-Body Quantum Mechanics / Niels Benedikter". Bonn : Universitäts- und Landesbibliothek Bonn, 2014. http://d-nb.info/1052061079/34.
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Brandao, Fernando G. S. L. "Entanglement theory and the quantum simulation of many-body physics". Thesis, Imperial College London, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491112.
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Quantum mechanics led us to reconsider the scope of physics and its building principles, such as the notions of realism and locality. More recently, quantum mechanics has changed in an equal dramatic manner our understanding of information processing and computation. On one hand, the fundamental properties of quantum systems can be harnessed to transmit, store, and manipulate information in a much more efficient and secure way than possible in the realm of classical physics. On the other hand, the development of systematic procedures to manipulate systems of a large number of particles in the quantum regime, crucial to the implementation of quantum based information processing, has triggered new possibilities in the exploration of quantum many-body physics and related areas. In this thesis, we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement, intrinsically quantum correlations of key importance in quantum information theory, and the exploration of the use of controlled quantum systems to the computation and simulation of quantum many-body phenomena. In the first part we introduce a new approach to the study of entanglement by considering its manipulation under operations not capable of generating entanglement. In this setting we show how the landscape of entanglement conversion is reduced to the simplest situation possible: one unique measure completely specifying which transformations are achievable. This framework has remarkable connections with the foundations of thermodynamics, which we present and explore. On the way to establish our main result, we develop new techniques that are of interest on their own. First, we extend quantum Stein's Lemma, characterizing optimal rates in state discrimination, to the case where the alternative hypothesis might vary over particular sets of possibly correlated (non-LLd) states. Second, we show how recent advances in quantum de Finetti type theorems can be employed to decide when the entanglement contained in non-LLd. sequences of states is distillable by local operations and classical communication. In the second part we discuss the usefulness of a quantum computer to the determination of properties of many-body systems. Our first result is a new quantum procedure, based on the phase estimation quantum algorithm, to calculate additive approximations to partition functions and spectrum densities of quantum local Hamiltonians. We give convincing evidence that quantum computation is superior to classical in solving both problems by showing that they are complete for the class of problems efficiently solved in the one-c1ean-qubit model of quantum computation, which is believe to contain classically hard problems. We then present a negative result on the usefulness of quantum computers and prove that the determination of the ground state energy of local quantum Hamiltonians, with the promise that the gap is larger than an inverse polynomial in the number of sites, is hard for the class QCMA, which is believed to contain intractable problems even for quantum computation. In the third and last part, we approach the problem of quantum simulating many-body systems from a more pragmatic point of view. Based on recent experimental developments on cavity quantum electrodynamics, more specifically on the fabrication of arrays of interacting micro-cavities and on their coupling to atomic-like structures in several physical set-ups, we propose and analyse the realization of paradigmatic condensed matter models in such systems, such as the Bose-Hubbard and the anisotropic Heisenberg models. We present· promising properties of such coupled-cavity arrays as simulators of quantum many-body physics, such as the full addressability of individual sites and the access to inhomogeneous models, and discuss the feasibility of an experimental realization with state-of-the-art current technology.
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Kshetrimayum, Augustine [Verfasser]. "Quantum many-body systems and Tensor Network algorithms / Augustine Kshetrimayum". Mainz : Universitätsbibliothek Mainz, 2018. http://d-nb.info/1158525427/34.
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Lee, Derek Kwok Kay. "Many-body phenomena in inhomogeneous and low-dimensional quantum liquids". Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358646.
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Buyskikh, Anton S. "Dynamics of quantum many-body systems with long-range interactions". Thesis, University of Strathclyde, 2017. http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=28798.
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Constantly increasing experimental possibilities with strongly correlated systems of ultracold atoms in optical lattices and trapped ions make them one of the most promising candidates for quantum simulation and quantum computation in the near future, and open new opportunities for study many-body physics. Out-of-equilibrium properties of such complex systems present truly fascinating and rich physics, which is yet to be fully understood. This thesis studies many-body dynamics of quantum systems with long-range interactions and addresses a few distinct issues. The first one is related to a growing interest in the use of ultracold atoms in optical lattices to simulate condensed matter systems, in particular to understand their magnetic properties. In our project on tilted optical lattices we map the dynamics of bosonic particles with resonantly enhanced long-range tunnelings onto a spin chain with peculiar interaction terms. We study the novel properties of this system in and out of equilibrium. The second main topic is the dynamical growth of entanglement and spread of correlations between system partitions in quench experiments. Our investigation is based on current experiments with trapped ions, where the range of interactions can be tuned dynamically from almost neighboring to all-to-all. We analyze the role of this interaction range in non-equilibrium dynamics. The third topic we address is a new method of quantum state estimation, certified Matrix Product State (MPS) tomography, which has potential applications in regimes unreachable by full quantum state tomography. The investigation of quantum many-body systems often goes beyond analytically solvable models; that is where numerical simulations become vital. The majority of results in this thesis were obtained via the Density Matrix Renormalization Group (DMRG) methods in the context of the MPS and Matrix Product Operator(MPO) formalism. Further developing and optimizing these methods made it possible to obtain eigenstates and thermal states as well as to calculate the time dependent dynamics in quenches for experimentally relevant regimes.
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Movassagh, Ramis. "Eigenvalues and low energy eigenvectors of quantum many-body systems". Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/73370.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 211-221).
I first give an overview of the thesis and Matrix Product States (MPS) representation of quantum spin systems on a line with an improvement on the notation. The rest of this thesis is divided into two parts. The first part is devoted to eigenvalues of quantum many-body systems (QMBS). I introduce Isotropic Entanglement (IE) and show that the distribution of QMBS with generic interactions can be accurately obtained using IE. Next, I discuss the eigenvalue distribution of one particle hopping random Schrbdinger operator in one dimension from free probability theory in context of the Anderson model. The second part is devoted to ground states and gap of QMBS. I first give the necessary background on frustration free Hamiltonians, real and imaginary time evolution of quantum spin systems on a line within MPS representation and the numerical implementation. I then prove the degeneracy and unfrustration condition for quantum spin chains with generic local interactions. Following this, I summarize my efforts in proving lower bounds for the entanglement of the ground states, which includes partial results, with the hope that it will inspire future work resulting in solving the conjecture given. Next I discuss two interesting measure zero examples where the Hamiltonians are carefully constructed to give unique ground states with high entanglement. This includes exact calculations of Schmidt numbers, entanglement entropies and a novel technique for calculating the gap. The last chapter elaborates on one of the measure zero examples (i.e., d = 3) which is the first example of a Frustration Free translation-invariant spin-i chain that has a unique highly entangled ground state and exhibits signatures of a critical behavior.
by Ramis Movassagh.
Ph.D.
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Dabelow, Lennart [Verfasser]. "Predicting quantum many-body dynamics out of equilibrium / Lennart Dabelow". Bielefeld : Universitätsbibliothek Bielefeld, 2021. http://d-nb.info/1228072701/34.
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Hoban, M. J. "Computational perspectives on Bell Inequalities and many-body quantum correlations". Thesis, University College London (University of London), 2012. http://discovery.ucl.ac.uk/1348376/.
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The predictions of quantum mechanics cannot be resolved with a completely classical view of the world. In particular, the statistics of space-like separated measurements on entangled quantum systems violate a Bell inequality [Bell1964]. We put forward a computational perspective on a broad class of Bell tests that study correlators, or the statistics of joint measurement outcomes. We associate particular maps, or functions to particular theories. The violation of a Bell inequality then implies the ability to perform some functions, or computations that classical, or more generally, local hidden variable (LHV) theories cannot. We derive an infinite class of Bell inequalities that establish a link to so-called "non-local games" [Cleve2004]. We then make the connection between Raussendorf and Briegel's formulation of Measurement-based Quantum Computing (MBQC) [Raussendorf2001], and these non-local games. Not only can we show that a quantum violation implies a computational advantage in this model, we show that adaptive measurements are required to perform all quantum computations. Finally, we explore post-selection of data in Bell tests from both a practical and conceptual point-of-view, with particular consideration to so-called "loopholes". Loopholes allow LHV theories to simulate quantum correlations through post-selection. We give a computational description of how loopholes can emerge in different post-selection scenarios. This motivates us to find a form of post-selection that does not lead to loopholes. Central again to this discussion is the description of LHV theories in terms of computations. Interestingly, quantum correlators can be made more "non-classical" with this loophole-free post-selection. This method of post-selection also can simulate information processing tasks, such as MBQC, that have time-like separated components. This opens up new avenues for the study of time-like tasks studied within the space-like separated scenario of the Bell test.
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Gerster, Matthias [Verfasser]. "Tensor network methods for quantum many-body simulations / Matthias Gerster". Ulm : Universität Ulm, 2021. http://d-nb.info/1233737406/34.
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Kozarzewski, Maciej. "Transport properties of disordered quantum chains with many-body interactions". Doctoral thesis, Katowice : Uniwersytet Śląski, 2020. http://hdl.handle.net/20.500.12128/20351.
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Systemy z lokalizacją wielociałową (ang. many-body localization, w skrócie
MBL) wykazują wiele
nietypowych zachowań, ale przez długi czas były tematem jedynie teoretycznych (lub
numerycznych) badań. Kilka lat temu możliwe stało się tworzenie takich układów w
laboratorium i eksperymentalne zweryfikowanie ich własności, co z kolei stymulowało
powstawanie kolejnych prac teoretycznych.
Rozprawa dotyczy własności transportowych jednowymiarowych układów
MBL. Skupiamy się na jednowymiarowym układzie bezspinowych fermionów z
nieporządkiem, do którego przyłożono zewnętrzne pole magnetyczne. To pole
wywołuje oscylacje Blocha, ale pokazujemy, że dla silnego nieporządku ich
częstotliwość jest stała i niezależna od pozostałych parametrów. Co więcej, zanik prądu
jest wynikiem destruktywnej interferencji prądów płynących między sąsiednimi
węzłami. Co ciekawe, te lokalne prądy nie wykazują żadnego tłumienia, co wskazuje
na to, że MBL zapobiega nagrzewaniu się takich układów.
Następnie przenosimy się do układów ze spinem 1/2, konkretnie modelu
Hubbarda z nieporządkiem. Trwa ciągła dyskusja na temat tego, czy nieporządek w
sektorze ładunków może wywołać pełną lokalizację. Tworzymy efektywny model
spinowy zakładając, że ładunki są nieruchome. W ramach modelu efektywnego
pokazujemy, że faktycznie pełna lokalizacja nie jest możliwa bez wprowadzania
dodatkowego nieporządku w sektorze spinowym. Badamy też transport
energii i okazuje się, że jest on stłumiony. Wprawdzie możemy wykluczyć, że jest to
efekt skończonego rozmiaru układu, ale i tak kontrastuje to z relatywnie szybką
relaksacją spinu.
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Raghunandan, Meghana [Verfasser]. "Quantum technological applications using dissipative many-body dynamics / Meghana Raghunandan". Hannover : Gottfried Wilhelm Leibniz Universität Hannover, 2020. http://d-nb.info/1211724018/34.
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Trujillo, Alba Marcela Herrera. "Quantum heat engines and energy fluctuations in many-body systems". reponame:Repositório Institucional da UFABC, 2017.
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Schiulaz, Mauro. "Ideal quantum glass transitions: many-body localization without quenched disorder?" Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4908.
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In this work the role of disorder, interaction and temperature in the physics of quantum non-ergodic systems is discussed. I first review what is meant by thermalization in closed quantum systems, and how ergodicity is violated in the presence of strong disorder, due to the phenomenon of Anderson localization. I explain why localization can be stable against the addition of weak dephasing interactions, and how this leads to the very rich phenomenology associated with many-body localization. I also briefly compare localized systems with their closest classical analogue, which are glasses, and discuss their similarities and differences, the most striking being that in quantum systems genuine non ergodicity can be proven in some cases, while in classical systems it is a matter of debate whether thermalization eventually takes place at very long times.
Up to now, many-body localization has been studies in the region of strong disorder and weak interaction. I show that strongly interacting systems display phenomena very similar to localization, even in the absence of disorder. In such systems, dynamics starting from a random inhomogeneous initial condition are non-perturbatively slow, and relaxation takes place only in exponentially long times. While in the thermodynamic limit ergodicity is ultimately restored due to rare events, from the practical point of view such systems look as localized on their initial condition, and this behavior can be studied experimentally. Since their behavior shares similarities with both many-body localized and classical glassy systems, these models are termed “quantum glasses”.
Apart from the interplay between disorder and interaction, another important issue concerns the role of temperature for the physics of localization. In non-interacting systems, an energy threshold separating delocalized and localized states exist, termed “mobility edge”. It is commonly believed that a mobility edge should exist in interacting systems, too. I argue that this scenario is inconsistent because inclusions of the ergodic phase in the supposedly localized phase can serve as mobile baths that induce global delocalization. I conclude that true non-ergodicity can be present only if the whole spectrum is localized. Therefore, the putative transition as a function of temperature is reduced to a sharp crossover. I numerically show that the previously reported mobility edges can not be distinguished from finite size effects. Finally, the relevance of my results for realistic experimental situations is discussed.
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Sardharwalla, Imdad Sajjad Badruddin. "Topics in computing with quantum oracles and higher-dimensional many-body systems". Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/264956.
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Since they were first envisioned, quantum computers have oft been portrayed as devices of limitless power, able to perform calculations in a mere instant that would take current computers years to determine. This is, of course, not the case. A huge amount of effort has been invested in trying to understand the limits of quantum computers---under which circumstances they outperform classical computers, how large a speed-up can be gained, and what draws the distinction between quantum and classical computing. In this Ph.D. thesis, I investigate a few intriguing properties of quantum computers involving quantum oracles and classically-simulatable quantum circuits. In Part I I study the notion of black-box unitary operations, and procedures for effecting the inverse operation. Part II looks at how quantum oracles can be used to test properties of probability distributions, and Part III considers classes of quantum circuits that can be simulated efficiently on a classical computer. In more detail, Part I studies procedures for inverting black-box unitary operations. Known techniques are generally limited in some way, often requiring ancilla systems, working only for restricted sets of operators, or simply being too inefficient. We develop a novel procedure without these limitations, and show how it can be applied to lift a requirement of the Solovay-Kitaev theorem, a landmark theorem of quantum compiling. Part II looks at property testing for probability distributions, and in particular considers a special type of access known as the \textit{conditional oracle}. The classical conditional oracle was developed by Canonne et al. in 2015 and subsequently greatly explored. We develop a quantum version of this oracle, and show that it has advantages over the classical process. We use this oracle to develop an algorithm that decides whether or not a mixed state is fully mixed. In Part III we study classically-simulatable quantum circuits in more depth. Two well-known classes are Clifford circuits and matchgate circuits, which we briefly review. Using these as inspiration, we use the Jordan-Wigner transform to develop new classes of non-trivial quantum circuits that are also classically simulatable.
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Khan, Imran. "QUANTUM THEORY OF MANY BOSE ATOM SYSTEMS". Connect to Online Resource-OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=Toledo1195507917.
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Friesdorf, Mathis [Verfasser]. "Closed quantum many-body systems out of equilibrium : A quantum information perspective / Mathis Friesdorf". Berlin : Freie Universität Berlin, 2016. http://d-nb.info/1099282829/34.
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