Relevant bibliographies by topics / Quantum Mechanics - Many Body Problems

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Quantum Mechanics - Many Body Problems'

Author: Grafiati
Published: 7 September 2023

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Journal articles on the topic "Quantum Mechanics - Many Body Problems"

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ALBEVERIO, SERGIO, LUDWIK DABROWSKI, and SHAO-MING FEI. "A REMARK ON ONE-DIMENSIONAL MANY-BODY PROBLEMS WITH POINT INTERACTIONS." International Journal of Modern Physics B 14, no. 07 (March 20, 2000): 721–27. http://dx.doi.org/10.1142/s0217979200000601.

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The integrability of one-dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) δ-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics.
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Herrera, William J., Herbert Vinck-Posada, and Shirley Gómez Páez. "Green's functions in quantum mechanics courses." American Journal of Physics 90, no. 10 (October 2022): 763–69. http://dx.doi.org/10.1119/5.0065733.

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The use of Green's functions is valuable when solving problems in electrodynamics, solid-state physics, and many-body physics. However, its role in quantum mechanics is often limited to the context of scattering by a central force. This work shows how Green's functions can be used in other examples in quantum mechanics courses. In particular, we introduce time-independent Green's functions and the Dyson equation to solve problems with an external potential. We calculate the reflection and transmission coefficients of scattering by a Dirac delta barrier and the energy levels and local density of states of the infinite square well potential.
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Wu, Yueyang. "A New Simple Method of Simulating One Dimensional Quantum Problem Based on Lattice Point Concepts." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 461–69. http://dx.doi.org/10.54097/hset.v38i.5868.

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One-dimensional quantum problems have always been an important issue in various branches of quantum mechanics fields, and many quantum models can be idealized as one-dimensional potential profiles. Therefore, it is necessary to investigates the way to deal with and calculate the problems. This paper proposes a new and simple method for simulation and calculation of one-dimensional quantum problems. To be specific, by representing continuous X values by a series of discrete lattice points, the Hamiltonian matrix is constructed for the system in the way of dealing with monomer and many-body problems, so as to simply calculate the energy level distribution and draw the wave function image. In terms of simulating one-dimensional infinite deep potential well, one-dimensional finite deep potential well, one-dimensional multi-potential well and other one-dimensional quantum systems with this method, this paper shows that the method is accurate and practical. Compared with other methods for one-dimensional quantum problems, this paper also presents the superiority of this method. To deal with the problem based on such a method can save the computation cost and time cost, which is more convenient to study the one-dimensional quantum problem in the future. These results shed light on studying complex one-dimensional quantum problems conveniently.
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Meisinger, Peter N., and Michael C. Ogilvie. "PT symmetry in classical and quantum statistical mechanics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (April 28, 2013): 20120058. http://dx.doi.org/10.1098/rsta.2012.0058.

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-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. -symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviours than Hermitian systems, displaying sinusoidally modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with -symmetry include Z( N ) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbour Ising model. Quantum many-body problems with a non-zero chemical potential have a natural -symmetric representation related to the sign problem. Two-dimensional quantum chromodynamics with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate -symmetric Hamiltonian.
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Wu, Yusen, and Jingbo B. Wang. "Estimating Gibbs partition function with quantum Clifford sampling." Quantum Science and Technology 7, no. 2 (February 14, 2022): 025006. http://dx.doi.org/10.1088/2058-9565/ac47f0.

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Abstract The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum systems and phenomena. However, for interacting many-body quantum systems, its calculation generally involves summing over an exponential number of terms and can thus quickly grow to be intractable. Accurately and efficiently estimating the partition function of its corresponding system Hamiltonian then becomes the key in solving quantum many-body problems. In this paper we develop a hybrid quantum–classical algorithm to estimate the partition function, utilising a novel quantum Clifford sampling technique. Note that previous works on the estimation of partition functions require O ( 1 / ϵ Δ ) -depth quantum circuits (Srinivasan et al 2021 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) pp 112–22; Montanaro 2015 Proc. R. Soc. A 471 20150301), where Δ is the minimum spectral gap of stochastic matrices and ϵ is the multiplicative error. Our algorithm requires only a shallow O ( 1 ) -depth quantum circuit, repeated O ( n / ϵ 2 ) times, to provide a comparable ϵ approximation. Shallow-depth quantum circuits are considered vitally important for currently available noisy intermediate-scale quantum devices.
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KUZEMSKY, A. L. "BOGOLIUBOV'S VISION: QUASIAVERAGES AND BROKEN SYMMETRY TO QUANTUM PROTECTORATE AND EMERGENCE." International Journal of Modern Physics B 24, no. 08 (March 30, 2010): 835–935. http://dx.doi.org/10.1142/s0217979210055378.

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In the present interdisciplinary review, we focus on the applications of the symmetry principles to quantum and statistical physics in connection with some other branches of science. The profound and innovative idea of quasiaverages formulated by N. N. Bogoliubov, gives the so-called macro-objectivation of the degeneracy in the domain of quantum statistical mechanics, quantum field theory and quantum physics in general. We discuss the complementary unifying ideas of modern physics, namely: spontaneous symmetry breaking, quantum protectorate and emergence. The interrelation of the concepts of symmetry breaking, quasiaverages and quantum protectorate was analyzed in the context of quantum theory and statistical physics. The chief purposes of this paper were to demonstrate the connection and interrelation of these conceptual advances of the many-body physics and to try to show explicitly that those concepts, though different in details, have certain common features. Several problems in the field of statistical physics of complex materials and systems (e.g., the chirality of molecules) and the foundations of the microscopic theory of magnetism and superconductivity were discussed in relation to these ideas.
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Sattath, Or, Siddhardh C. Morampudi, Chris R. Laumann, and Roderich Moessner. "When a local Hamiltonian must be frustration-free." Proceedings of the National Academy of Sciences 113, no. 23 (May 19, 2016): 6433–37. http://dx.doi.org/10.1073/pnas.1519833113.

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A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion—a sufficient condition—under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer’s theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian’s interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.
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Holland, Peter. "Uniting the wave and the particle in quantum mechanics." Quantum Studies: Mathematics and Foundations 7, no. 1 (October 5, 2019): 155–78. http://dx.doi.org/10.1007/s40509-019-00207-4.

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Abstract We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie–Bohm theory: its reliance on the quantum probability formula to justify the particle-guidance equation; its insouciance regarding the absence of reciprocal action of the particle on the guiding wavefunction; and its lack of a unified model to represent its inseparable components. Following the author’s previous work, these problems are examined within an analytical framework by requiring that the wave–particle composite exhibits no observable differences with a quantum system. This scheme is implemented by appealing to symmetries (global gauge and spacetime translations) and imposing equality of the corresponding conserved Noether densities (matter, energy, and momentum) with their Schrödinger counterparts. In conjunction with the condition of time-reversal covariance, this implies the de Broglie–Bohm law for the particle where the quantum potential mediates the wave–particle interaction (we also show how the time-reversal assumption may be replaced by a statistical condition). The method clarifies the nature of the composite’s mass, and its energy and momentum conservation laws. Our principal result is the unification of the Schrödinger equation and the de Broglie–Bohm law in a single inhomogeneous equation whose solution amalgamates the wavefunction and a singular soliton model of the particle in a unified spacetime field. The wavefunction suffers no reaction from the particle since it is the homogeneous part of the unified field to whose source the particle contributes via the quantum potential. The theory is extended to many-body systems. We review de Broglie’s objections to the pilot-wave theory and suggest that our field-theoretic description provides a realization of his hitherto unfulfilled ‘double solution’ programme. A revised set of postulates for the de Broglie–Bohm theory is proposed in which the unified field is taken as the basic descriptive element of a physical system.
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Yung, Man-Hong, Xun Gao, and Joonsuk Huh. "Universal bound on sampling bosons in linear optics and its computational implications." National Science Review 6, no. 4 (April 9, 2019): 719–29. http://dx.doi.org/10.1093/nsr/nwz048.

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ABSTRACT In linear optics, photons are scattered in a network through passive optical elements including beam splitters and phase shifters, leading to many intriguing applications in physics, such as Mach–Zehnder interferometry, the Hong–Ou–Mandel effect, and tests of fundamental quantum mechanics. Here we present the fundamental limit in the transition amplitudes of bosons, applicable to all physical linear optical networks. Apart from boson sampling, this transition bound results in many other interesting applications, including behaviors of Bose–Einstein condensates (BEC) in optical networks, counterparts of Hong–Ou–Mandel effects for multiple photons, and approximating permanents of matrices. In addition, this general bound implies the existence of a polynomial-time randomized algorithm for estimating the transition amplitudes of bosons, which represents a solution to an open problem raised by Aaronson and Hance (Quantum Inf Comput 2012; 14: 541–59). Consequently, this bound implies that computational decision problems encoded in linear optics, prepared and detected in the Fock basis, can be solved efficiently by classical computers within additive errors. Furthermore, our result also leads to a classical sampling algorithm that can be applied to calculate the many-body wave functions and the S-matrix of bosonic particles.
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Movassagh, Ramis, and Peter W. Shor. "Supercritical entanglement in local systems: Counterexample to the area law for quantum matter." Proceedings of the National Academy of Sciences 113, no. 47 (November 7, 2016): 13278–82. http://dx.doi.org/10.1073/pnas.1605716113.

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Quantum entanglement is the most surprising feature of quantum mechanics. Entanglement is simultaneously responsible for the difficulty of simulating quantum matter on a classical computer and the exponential speedups afforded by quantum computers. Ground states of quantum many-body systems typically satisfy an “area law”: The amount of entanglement between a subsystem and the rest of the system is proportional to the area of the boundary. A system that obeys an area law has less entanglement and can be simulated more efficiently than a generic quantum state whose entanglement could be proportional to the total system’s size. Moreover, an area law provides useful information about the low-energy physics of the system. It is widely believed that for physically reasonable quantum systems, the area law cannot be violated by more than a logarithmic factor in the system’s size. We introduce a class of exactly solvable one-dimensional physical models which we can prove have exponentially more entanglement than suggested by the area law, and violate the area law by a square-root factor. This work suggests that simple quantum matter is richer and can provide much more quantum resources (i.e., entanglement) than expected. In addition to using recent advances in quantum information and condensed matter theory, we have drawn upon various branches of mathematics such as combinatorics of random walks, Brownian excursions, and fractional matching theory. We hope that the techniques developed herein may be useful for other problems in physics as well.
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Dissertations / Theses on the topic "Quantum Mechanics - Many Body Problems"

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Lentz, Simon. "Exact eigenstates of the Inozemtsev spin chain." Thesis, KTH, Fysik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297571.

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This thesis deals with the following question: are there more eigenfunctions, other than the already known eigenfunctions, of the spin chain with elliptic interactions known as the Inozemtsev spin chain? The Inozemtsev spin chain interpolates between two quantum integrable spin chains, theHeisenberg spin chain and the Haldane-Shastry spin chain. Therefore it is interesting to explore eigenfunctions of the Inozemtsev spin chain in greater detail. Moreover, there exists connections between spin chains and their corresponding spinless continuum model, namely theCalogero-Sutherland models; a derivation of the connection between the Haldane-Shastry spin chain and the trigonometric interacting Calogero-Sutherland model is presented in this thesis. These connections state that the eigenfunctions of the Calogero-Sutherland model are also eigenfunctionsof the corresponding spin chain. An established connection between the Inozemtsev spin chain and the elliptic interacting Calogero-Sutherland model yields exact eigenfunctions with simple poles at coinciding arguments of the Inozemtsev spin chain. However, there are eigenfunctions of theelliptic Calogero-Sutherland model with second order zeros instead of simple poles at coinciding arguments. It is therefore interesting to see if a connection exists that relates the eigenfunctions of the elliptic Calogero-Sutherland model with second order zeros to eigenfunctionsof the Inozemtsev spin chain also with second order zeros. The main goal of this thesis is to explore eigenfunctions of the Inozemtsev spin chain with second order zeros for two magnons. This thesis uses analytical methods for finding these eigenfunctions and numerical methods have beenresorted to in the end. The numerical results indicate that the functions explored in this thesis fail to parametrise the eigenfunctions of the Inozemtsev spin chain, except for a few special cases.
Den här avhandlingen behandlar följande frågeställning: finns det fler egenfunktioner än de redan kända till spinnkedjan med elliptisk växelverkan känd som Inozemtsevs spinnkedja? Inozemtsevs spinnkedja interpolerar mellan Heisenbergs spinnkedja och Haldane-Shastrys spinnkedja som båda ärkvant-integrerbara. Därför är det intressant att vidare utforska egenfunktionerna hos Inozemtsevs spinnkedja. Det finns kopplingar mellan spinnkedjor och spinnfria en-dimensionella kontinuumsystem, nämligen Calogero-Sutherlands system; en sådan koppling mellan Haldane-Shastrysspinnkedja och Calogero-Sutherlands modell med trigonometrisk växelverkan härleds i denna avhandling. Dessa kopplingar konstaterar att egenfunktionerna för Calogero-Sutherland systemet är egenfunktioner för spinnkedjan också. En koppling existerar mellan Calogero-Sutherland modellen med elliptisk växelverkan och Inozemtsevs spinnkedja vilket ger exakta egenfunktioner hos Inozemtsevs modell med enkla poler vid sammanfallande argument. Däremot existerar det egenfunktioner till Calogero-Sutherland modellen med elliptisk växelverkan med andra ordningens nollor vid sammanfallande argument istället för enkla poler. Det är därför intressant att undersöka om det existerar en koppling mellan dessa två system med egenfunktioner med andra ordningens nollor; det här skulle då ge exakta egenfunktioner till Inozemtsevs spinnkedja med andra ordningens nollor. Detta är huvudsyftet med avhandlingen. Egenfunktioner med andra ordningens nollor för två magnoner undersöks. Avhandlingen använder sig av analytisk metod och har prövats med numeriska metoder. De numeriska resultaten indikerar att de undersökta funktionerna i denna avhandling misslyckas med att parametrisera egenfunktionerna till Inozemtsevs spinnkedja förutom vissa specifika fall.
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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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Ricaud, Julien. "Symétrie et brisure de symétrie pour certains problèmes non linéaires." Thesis, Cergy-Pontoise, 2017. http://www.theses.fr/2017CERG0849.

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Cette thèse est consacrée à l'étude mathématique de deux systèmes quantiques décrits par des modèles non linéaires : le polaron anisotrope et les électrons d'un cristal périodique. Après avoir prouvé l'existence de minimiseurs, nous nous intéressons à la question de l'unicité pour chacun des deux modèles. Dans une première partie, nous montrons l'unicité du minimiseur et sa non-dégénérescence pour le polaron décrit par l'équation de Choquard--Pekar anisotrope, sous la condition que la matrice diélectrique du milieu est presque isotrope. Dans le cas d'une forte anisotropie, nous laissons la question de l'unicité en suspens mais caractérisons précisément les symétries pouvant être dégénérées. Dans une seconde partie, nous étudions les électrons d'un cristal dans le modèle de Thomas--Fermi--Dirac--Von~Weizsäcker périodique, en faisant varier le paramètre devant le terme de Dirac. Nous montrons l'unicité et la non-dégénérescence du minimiseur lorsque ce paramètre est suffisamment petit et mettons en évidence une brisure de symétrie lorsque celui-ci est grand
This thesis is devoted to the mathematical study of two quantum systems described by nonlinear models: the anisotropic polaron and the electrons in a periodic crystal. We first prove the existence of minimizers, and then discuss the question of uniqueness for both problems. In the first part, we show the uniqueness and nondegeneracy of the minimizer for the polaron, described by the Choquard--Pekar anisotropic equation, assuming that the dielectric matrix of the medium is almost isotropic. In the strong anisotropic setting, we leave the question of uniqueness open but identify the symmetry that can possibly be degenerate. In the second part, we study the electrons of a crystal in the periodic Thomas--Fermi--Dirac--Von~Weizsäcker model, varying the parameter in front of the Dirac term. We show uniqueness and nondegeneracy of the minimizer when this parameter is small enough et prove the occurrence of symmetry breaking when it is large
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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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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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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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Bertini, Bruno. "Non-equilibrium dynamics of interacting many-body quantum systems in one dimension." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:1e2c50b9-73b3-4ca0-a5f3-276f967c3720.

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In this thesis we study three examples of interacting many-body systems undergoing a non equilibrium time evolution. Firstly we consider the time evolution in an integrable system: the sine-Gordon field theory in the repulsive regime. We will focus on the one point function of the semi-local vertex operator eiβφ(x)/2 on a specific class of initial states. By analytical means we show that the expectation value considered decays exponentially to zero at late times and we determine the decay time. The method employed is based on a form-factor expansion and uses the "Representative Eigenstate Approach" of Ref. [73] (a.k.a. "Quench Action"). In a second example we study the time evolution in models close to "special" integrable points characterised by hidden symmetries generating infinitely many local conservation laws that do not commute with one another, in addition to the infinite commuting family implied by integrability. We observe that both in the case where the perturbation breaks the integrability and when it breaks only the additional symmetries maintaining integrability, the local observables show a crossover behaviour from an initial to a final quasi stationary plateau. We investigate a weak coupling limit, identify a time window in which the effects of the perturbations become significant and solve the time evolution through a mean-field mapping. As an explicit example we study the XYZ spin-1/2 chain with additional perturbations that break integrability. Finally, we study the effects of integrability breaking perturbations on the non-equilibrium evolution of more general many-particle quantum systems, where the unperturbed integrable model is generic. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalisations of quantum Boltzmann equations. We benchmark our method against time dependent density matrix renormalisation group computations and find it to be very accurate as long as interactions are weak. For small integrability breaking, we observe robust prethermalisation plateaux for local observables on all accessible time scales. Increasing the strength of the integrability breaking term induces a "drift" away from the prethermalisation plateaux towards thermal behaviour. We identify a time scale characterising this crossover.
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Russomanno, Angelo. "Periodic driving of a coherent quantum many body system and relaxation to the Floquet diagonal ensemble." Doctoral thesis, SISSA, 2014. http://hdl.handle.net/20.500.11767/3904.

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The coherent dynamics of many body quantum system is nowadays an experimental reality: by means of the cold atoms in optical lattices, many Hamiltonians and time-dependent perturbations can be engineered. In this Thesis we discuss what happens in these systems when a periodic perturbation is applied. Thanks to Floquet theory, we can see that -- if the Floquet spectrum obeys certain continuity conditions possible in the thermodynamic limit-- dephasing among Floquet quasi-energies makes local observables relax to a periodic steady regime described by an effective density matrix: the Floquet diagonal ensemble (FDE). By means of numerical examples on the Quantum Ising Chain and the Lipkin model, we discuss the properties of the FDE focusing on the difference among ergodic and regular quantum dynamics and on how this reflects on the thermal properties ($T=\infty$) of the asymptotic condition. We verify thermalization in the classically ergodic Lipkin model and we demonstrate that this effect is induced by the Floquet states being delocalized and obeying Eigenstate Thermalization Hypothesis.We discuss also, in the Ising chain case, the work probability distribution, whose asymptotic condition is not described by the form (Generalized Gibbs Ensemble) that FDE acquires for local obserbvables because of integrability. Dephasing makes some correlations invisible in the local observables, but they are still present in the system. We consider also the linear response limit: when the amplitude of the perturbation is vanishingly small, the Floquet diagonal ensemble is not sufficient to describe the asymptotic condition given by LRT. For every small but finite amplitude, there are quasi-degeneracies in the Floquet spectrum giving rise to pre-relaxation to the condition predicted by Linear Response; these phenomena are strictly related to energy absorption and boundedness of the spectrum.
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Mucciolo, Eduardo Rezende. "Universal correlations in the quantum spectra of chaotic systems and exactly solvable many-body problems." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/35996.

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Hafver, Andreas. "The formalism of non-commutative quantum mechanics and its extension to many-particle systems." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/5255.

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Thesis (MSc (Physics))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: Non-commutative quantum mechanics is a generalisation of quantum mechanics which incorporates the notion of a fundamental shortest length scale by introducing non-commuting position coordinates. Various theories of quantum gravity indicate the existence of such a shortest length scale in nature. It has furthermore been realised that certain condensed matter systems allow effective descriptions in terms of non-commuting coordinates. As a result, non-commutative quantum mechanics has received increasing attention recently. A consistent formulation and interpretation of non-commutative quantum mechanics, which unambiguously defines position measurement within the existing framework of quantum mechanics, was recently presented by Scholtz et al. This thesis builds on the latter formalism, extends it to many-particle systems and links it up with non-commutative quantum field theory via second quantisation. It is shown that interactions of particles, among themselves and with external potentials, are altered as a result of the fuzziness induced by non-commutativity. For potential scattering, generic increases are found for the differential and total scattering cross sections. Furthermore, the recovery of a scattering potential from scattering data is shown to involve a suppression of high energy contributions, disallowing divergent interaction forces. Likewise, the effective statistical interaction among fermions and bosons is modified, leading to an apparent violation of Pauli’s exclusion principle and foretelling implications for thermodynamics at high densities.
AFRIKAANSE OPSOMMING: Nie-kommutatiewe kwantummeganika is ’n veralgemening van kwantummeganika wat die idee van ’n fundamentele kortste lengteskaal invoer d.m.v. nie-kommuterende ko¨ordinate. Verskeie teorie¨e van kwantum-grawitasie dui op die bestaan van so ’n kortste lengteskaal in die natuur. Dit is verder uitgewys dat sekere gekondenseerde materie sisteme effektiewe beskrywings in terme van nie-kommuterende koordinate toelaat. Gevolglik het die veld van nie-kommutatiewe kwantummeganika onlangs toenemende aandag geniet. ’n Konsistente formulering en interpretasie van nie-kommutatiewe kwantummeganika, wat posisiemetings eenduidig binne bestaande kwantummeganika raamwerke defineer, is onlangs voorgestel deur Scholtz et al. Hierdie tesis brei uit op hierdie formalisme, veralgemeen dit tot veeldeeltjiesisteme en koppel dit aan nie-kommutatiewe kwantumveldeteorie d.m.v. tweede kwantisering. Daar word gewys dat interaksies tussen deeltjies en met eksterne potensiale verander word as gevolg van nie-kommutatiwiteit. Vir potensiale verstrooi ¨ıng verskyn generiese toenames vir die differensi¨ele and totale verstroi¨ıngskanvlak. Verder word gewys dat die herkonstruksie van ’n verstrooi¨ıngspotensiaal vanaf verstrooi¨ıngsdata ’n onderdrukking van ho¨e-energiebydrae behels, wat divergente interaksiekragte verbied. Soortgelyk word die effektiewe statistiese interaksie tussen fermione en bosone verander, wat ly tot ’n skynbare verbreking van Pauli se uitsluitingsbeginsel en dui op verdere gevolge vir termodinamika by ho¨e digthede.
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Books on the topic "Quantum Mechanics - Many Body Problems"

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March, Norman H. The many-body problem in quantum mechanics. New York: Dover Publications, 1995.

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Many-body problems and quantum field theory. New York: Springer, 2001.

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Van, Neck Dimitri, ed. Many-body theory exposed!: Propagator description of quantum mechanics in many-body systems. 2nd ed. Hackensack, NJ: World Scientific, 2008.

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Van, Neck Dimitri, ed. Many-body theory exposed!: Propagator description of quantum mechanics in many-body systems. Hackensack, NJ: World Scientific, 2005.

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Dickhoff, Willem Hendrik. Many-body theory exposed!: Propagator description of quantum mechanics in many-body systems. Singapore: World Scientific, 2006.

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M, Eisenberg Judah, ed. Quantum mechanics of many degrees of freedom. New York: Wiley, 1988.

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Bethe, Hans Albrecht. Quantum mechanics of one- and two-electron atoms. Mineola, N.Y: Dover Publications, 2008.

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Trump, M. A. Classical Relativistic Many-Body Dynamics. Dordrecht: Springer Netherlands, 1999.

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Mathematical methods of many-body quantum field theory. Boca Raton: Chapman & Hall/CRC, 2005.

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Kadanoff, Leo P. Quantum statistical mechanics: Green's function methods in equilibrium and nonequilibrium problems. Redwood City, Calif: Addison-Wesley Pub. Co., Advanced Book Program, 1989.

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Book chapters on the topic "Quantum Mechanics - Many Body Problems"

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Bes, Daniel R. "Many-Body Problems." In Quantum Mechanics, 95–118. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05384-3_7.

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Bes, Daniel R. "Many-Body Problems." In Quantum Mechanics, 109–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20556-9_7.

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Flügge, Siegfried. "IV. Many-Body Problems." In Practical Quantum Mechanics, 379–470. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-61995-3_4.

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Greiner, Walter. "Elementary Aspects of the Quantum-Mechanical Many-Body Problem." In Quantum Mechanics, 335–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57974-5_14.

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Greiner, Walter. "Elementary Aspects of the Quantum-Mechanical Many-Body Problem." In Quantum Mechanics, 367–401. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56826-8_14.

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Greiner, Walter. "Elementary Aspects of the Quantum-Mechanical Many-Body Problem." In Quantum Mechanics, 259–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-00707-5_14.

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Greiner, Walter. "Elementary Aspects of the Quantum-Mechanical Many-Body Problem." In Quantum Mechanics, 259–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-30374-0_14.

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Lee, T. D., and C. N. Yang. "Many-Body Problem in Quantum Mechanics and Quantum Statistical Mechanics." In Selected Papers, 545–46. Boston, MA: Birkhäuser Boston, 1986. http://dx.doi.org/10.1007/978-1-4612-5397-6_39.

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Verbeure, A., and V. A. Zagrebnov. "Quantum Fluctuations in the Many-Body Problem." In Mathematical Results in Quantum Mechanics, 207–12. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8545-4_25.

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Lee, T. D., and C. N. Yang. "Many-Body Problem in Quantum Statistical Mechanics. I. General Formulation." In Selected Papers, 581–93. Boston, MA: Birkhäuser Boston, 1986. http://dx.doi.org/10.1007/978-1-4612-5397-6_44.

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Conference papers on the topic "Quantum Mechanics - Many Body Problems"

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Wessels, V. "Euclidean relativistic quantum mechanics." In FEW-BODY PROBLEMS IN PHYSICS: The 19th European Conference on Few-Body Problems in Physics. AIP, 2005. http://dx.doi.org/10.1063/1.1932974.

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Desplanques, B. "A relativistic quantum mechanics approach inspired by the Dirac’s point form." In FEW-BODY PROBLEMS IN PHYSICS: The 19th European Conference on Few-Body Problems in Physics. AIP, 2005. http://dx.doi.org/10.1063/1.1932970.

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Zhao, Xuncheng, Mingfan Li, Qian Xiao, Junshi Chen, Fei Wang, Li Shen, Meijia Zhao, et al. "AI for Quantum Mechanics: High Performance Quantum Many-Body Simulations via Deep Learning." In SC22: International Conference for High Performance Computing, Networking, Storage and Analysis. IEEE, 2022. http://dx.doi.org/10.1109/sc41404.2022.00053.

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"General Problems of Quantum Kinetic Theory." In Proceedings of the Conference “Kadanoff-Baym Equations: Progress and Perspectives for Many-Body Physics”. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812793812_others02.

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Fujita, M. "New Canonical Transformations to Eliminate External Fields in Quantum Many-Body Problems." In SLOW DYNAMICS IN COMPLEX SYSTEMS: 3rd International Symposium on Slow Dynamics in Complex Systems. AIP, 2004. http://dx.doi.org/10.1063/1.1764294.

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FORBERT, H. A., and S. A. CHIN. "A FOURTH ORDER DIFFUSION MONTE CARLO ALGORITHM FOR SOLVING QUANTUM MANY-BODY PROBLEMS." In Proceedings of the 10th International Conference. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792754_0056.

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DEAN, D. J. "COMPUTATIONAL CHALLENGES OF QUANTUM MANY-BODY PROBLEMS IN NUCLEAR STRUCTURE: COUPLED-CLUSTER THEORY." In Proceedings of the Symposium in Honor of Jerry P Draayer's 60th Birthday. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812703026_0016.

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Yamada, Susumu, Toshiyuki Imamura, Takuma Kano, and Masahiko Machida. "Gordon Bell finalists I---High-performance computing for exact numerical approaches to quantum many-body problems on the earth simulator." In the 2006 ACM/IEEE conference. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1188455.1188504.

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Datta, Ranadev, and Debabrata Sen. "A B-Spline Time Domain Solution for the Forward Speed Diffraction Problems." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92080.

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A B-spline based panel method is developed for the solution of the forward speed diffraction problem in time-domain. The body geometry is defined by an open uniform B-spline, and the unknown potentials and the source strengths are described by the same B-spline basis functions. The 3D potential flow boundary value problem is formulated based on a transient (time domain) Green’s function. Computed results are validated by comparing them with a wide variety of available results, including 3D numerical computations and experimental results. The present method agrees well with published results. Many of the existing 3D codes for the forward speed ship motion problem require high computing resources. The present method is however capable of producing the time simulation results over long duration using only a presently available PC, which is the main advantage of the proposed development.
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Zhang, Sheguang, Kenneth M. Weems, Woei-Min Lin, Hongmei Yan, and Yuming Liu. "Application of a Quadratic Boundary Element Method to Ship Hydrodynamic Problems." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57187.

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This paper describes the implementation and application of a Quadratic Boundary Element Method (QBEM) to the 3-D, time domain potential flow solution of ship-wave hydrodynamic interaction problems. In QBEM, the geometry, singularity, and solution distributions on each panel are represented by bi-quadratic parametric functions defined by nine nodal values. QBEM has been shown to provide many theoretical advantages in accuracy and convergence versus the more conventional Constant Panel Method (CPM), but its application to real ship flow problems presents many challenges. This paper describes the implementation of QBEM into an existing time-domain ship motion and wave load prediction code, the Large Amplitude Motions Program (LAMP), and identifies and addresses some important numerical issues related to QBEM, such as mismatched grid points between neighboring panels, surface normal calculation on degenerate QBEM panels, the stability of the free surface and the solution and treatment of QBEM panels for body-nonlinear calculations. A number of practical cases are provided to compare QBEM with CPM and to validate QBEM against analytical solutions and experiments. The advantages of using QBEM for ship hydrodynamic problems and associated/unresolved numerical issues are also discussed.
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