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Academic literature on the topic 'Standard Equilibrium Quantum Systems'

Author: Grafiati

Published: 7 September 2023

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Journal articles on the topic "Standard Equilibrium Quantum Systems"

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Venuti, Lorenzo Campos, and Paolo Zanardi. "Theory of temporal fluctuations in isolated quantum systems." International Journal of Modern Physics B 29, no. 14 (May 22, 2015): 1530008. http://dx.doi.org/10.1142/s021797921530008x.

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When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This paper reviews the general theory of such temporal fluctuations. We first survey some results on the strength of such temporal fluctuations. For example temporal fluctuations are exponentially small in the system's volume for generic systems whereas they fall-off algebraically in integrable systems. We then concentrate on the so-called quench scenario where the system is driven out-of-equilibrium under the application of a sudden perturbation. For sufficiently small perturbations, temporal fluctuations of physical observables can be characterized in full generality and can be used as an effective tool to probe quantum criticality of the underlying model. In the off-critical region the distribution becomes Gaussian. Close to criticality the distribution becomes a universal function uniquely characterized by a single critical exponent, that we compute explicitly. This contrasts standard equilibrium quantum fluctuations for which the critical distribution depends on a numerable set of critical coefficients and is known only for limited examples. The possibility of using temporal fluctuations to determine pseudo-critical boundaries in optical lattice experiments is further reviewed.

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Álvarez-Estrada, Ramon F. "Approach to Equilibrium of Statistical Systems: Classical Particles and Quantum Fields Off-Equilibrium." Dynamics 3, no. 2 (June 13, 2023): 345–78. http://dx.doi.org/10.3390/dynamics3020020.

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Non-equilibrium evolution at absolute temperature T and approach to equilibrium of statistical systems in long-time (t) approximations, using both hierarchies and functional integrals, are reviewed. A classical non-relativistic particle in one spatial dimension, subject to a potential and a heat bath (hb), is described by the non-equilibrium reversible Liouville distribution (W) and equation, with a suitable initial condition. The Boltzmann equilibrium distribution Weq generates orthogonal (Hermite) polynomials Hn in momenta. Suitable moments Wn of W (using the Hn’s) yield a non-equilibrium three-term hierarchy (different from the standard Bogoliubov–Born–Green–Kirkwood–Yvon one), solved through operator continued fractions. After a long-t approximation, the Wn’s yield irreversibly approach to equilibrium. The approach is extended (without hb) to: (i) a non-equilibrium system of N classical non-relativistic particles interacting through repulsive short range potentials and (ii) a classical ϕ4 field theory (without hb). The extension to one non-relativistic quantum particle (with hb) employs the non-equilibrium Wigner function (WQ): difficulties related to non-positivity of WQ are bypassed so as to formulate approximately approach to equilibrium. A non-equilibrium quantum anharmonic oscillator is analyzed differently, through functional integral methods. The latter allows an extension to relativistic quantum ϕ4 field theory (a meson gas off-equilibrium, without hb), facing ultraviolet divergences and renormalization. Genuine simplifications of quantum ϕ4 theory at high T and large distances and long t occur; then, through a new argument for the field-theoretic case, the theory can be approximated by a classical ϕ4 one, yielding an approach to equilibrium.

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Žunkovič, Bojan, Alessandro Silva, and Michele Fabrizio. "Dynamical phase transitions and Loschmidt echo in the infinite-range XY model." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2069 (June 13, 2016): 20150160. http://dx.doi.org/10.1098/rsta.2015.0160.

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We compare two different notions of dynamical phase transitions in closed quantum systems. The first is identified through the time-averaged value of the equilibrium-order parameter, whereas the second corresponds to non-analyticities in the time behaviour of the Loschmidt echo. By exactly solving the dynamics of the infinite-range XY model, we show that in this model non-analyticities of the Loschmidt echo are not connected to standard dynamical phase transitions and are not robust against quantum fluctuations. Furthermore, we show that the existence of either of the two dynamical transitions is not necessarily connected to the equilibrium quantum phase transition.

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FEDOROVA, ANTONINA N., and MICHAEL G. ZEITLIN. "PATTERN FORMATION IN QUANTUM ENSEMBLES." International Journal of Modern Physics B 20, no. 11n13 (May 20, 2006): 1570–92. http://dx.doi.org/10.1142/s0217979206033875.

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We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from basic localized modes in various collective models arising from the quantum hierarchy of Wigner-von Neumann-Moyal-Lindblad equations, which are the result of "wignerization" procedure of classical BBGKY hierarchy. We present the explicit description of internal quantum dynamics by means of exact analytical/numerical computations.

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Chen, Tyler, and Yu-Chen Cheng. "Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems." Journal of Chemical Physics 157, no. 6 (August 14, 2022): 064106. http://dx.doi.org/10.1063/5.0099761.

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We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system + bath) is held in canonical thermal equilibrium by weak coupling with a “super-bath”. Our approach is a generalization of now standard typicality algorithms for computing the quantum expectation value of observables of bare quantum systems via trace estimators and Krylov subspace methods. In particular, our algorithm makes use of the fact that the reduced system density, when the bath is measured in a given random state, tends to concentrate about the corresponding thermodynamic averaged reduced system density. Theoretical error analysis and numerical experiments are given to validate the accuracy of our algorithm. Further numerical experiments demonstrate the potential of our approach for applications including the study of quantum phase transitions and entanglement entropy for long range interaction systems.

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Schmidt, Heinz-Jürgen, and Jochen Gemmer. "A Framework for Sequential Measurements and General Jarzynski Equations." Zeitschrift für Naturforschung A 75, no. 3 (March 26, 2020): 265–84. http://dx.doi.org/10.1515/zna-2019-0272.

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AbstractWe formulate a statistical model of two sequential measurements and prove a so-called J-equation that leads to various diversifications of the well-known Jarzynski equation including the Crooks dissipation theorem. Moreover, the J-equation entails formulations of the Second Law going back to Wolfgang Pauli. We illustrate this by an analytically solvable example of sequential discrete position–momentum measurements accompanied with the increase of Shannon entropy. The standard form of the J-equation extends the domain of applications of the standard quantum Jarzynski equation in two respects: It includes systems that are initially only in local equilibrium, and it extends this equation to the cases where the local equilibrium is described by microcanononical, canonical, or grand canonical ensembles. Moreover, the case of a periodically driven quantum system in thermal contact with a heat bath is shown to be covered by the theory presented here if the quantum system assumes a quasi-Boltzmann distribution. Finally, we shortly consider the generalised Jarzynski equation in classical statistical mechanics.

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Rodríguez, Antonio, Alessandro Pluchino, Ugur Tirnakli, Andrea Rapisarda, and Constantino Tsallis. "Nonextensive Footprints in Dissipative and Conservative Dynamical Systems." Symmetry 15, no. 2 (February 7, 2023): 444. http://dx.doi.org/10.3390/sym15020444.

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Despite its centennial successes in describing physical systems at thermal equilibrium, Boltzmann–Gibbs (BG) statistical mechanics have exhibited, in the last several decades, several flaws in addressing out-of-equilibrium dynamics of many nonlinear complex systems. In such circumstances, it has been shown that an appropriate generalization of the BG theory, known as nonextensive statistical mechanics and based on nonadditive entropies, is able to satisfactorily handle wide classes of anomalous emerging features and violations of standard equilibrium prescriptions, such as ergodicity, mixing, breakdown of the symmetry of homogeneous occupancy of phase space, and related features. In the present study, we review various important results of nonextensive statistical mechanics for dissipative and conservative dynamical systems. In particular, we discuss applications to both discrete-time systems with a few degrees of freedom and continuous-time ones with many degrees of freedom, as well as to asymptotically scale-free networks and systems with diverse dimensionalities and ranges of interactions, of either classical or quantum nature.

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GORDON, GOREN, NOAM EREZ, and GERSHON KURIZKI. "ZENO HEATING AND ANTI-ZENO COOLING BY FREQUENT QUANTUM MEASUREMENTS." International Journal of Quantum Information 07, supp01 (January 2009): 49–62. http://dx.doi.org/10.1142/s021974990900475x.

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We study disturbances of thermal equilibrium between two-level systems (TLS) and a bath by frequent and brief quantum measurements of the TLS energy-states. If the measurements induce either the Zeno or the anti-Zeno regime, namely, the slowdown or speedup of the TLS relaxation, then the resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for markovian baths. These anomalies allow for very fast control heating, cooling and state-purification (entropy reduction) of quantum systems much sooner than their thermal equilibration time.

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Abul-Magd, A. Y. "Superstatistics in Random Matrix Theory." Sultan Qaboos University Journal for Science [SQUJS] 17, no. 2 (December 1, 2012): 157. http://dx.doi.org/10.24200/squjs.vol17iss2pp157-169.

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Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. The last decade witnessed several attempts to extend RMT to describe quantum systems with mixed regular-chaotic dynamics. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors have presented other versions of the theory that keep base invariance at the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or by following the basic prescription of the recently suggested concept of superstatistics. The latter concept was introduced as a generalization of equilibrium thermodynamics to describe non-equilibrium systems by allowing the temperature to fluctuate. We here review the superstatistical generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments on billiards modeling systems in transition from order to chaos.

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Luo, Yu-Chen, and Xiao-Peng Li. "Quantum simulation of interacting fermions." Acta Physica Sinica 71, no. 22 (2022): 226701. http://dx.doi.org/10.7498/aps.71.20221756.

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Fermions are basic building blocks in the standard model. Interactions among these elementary particles determine how they assemble and consequently form various states of matter in our nature. Simulating fermionic degrees of freedom is also a central problem in condensed matter physics and quantum chemistry, which is crucial to understanding high-temperature superconductivity, quantum magnetism and molecular structure and functionality. However, simulating interacting fermions by classical computing generically face the minus sign problem, encountering the exponential computation complexity. Ultracold atoms provide an ideal experimental platform for quantum simulation of interacting fermions. This highly-controllable system enables the realizing of nontrivial fermionic models, by which the physical properties of the models can be obtained by measurements in experiment. This deepens our understanding of related physical mechanisms and help determine the key parameters. In recent years, there have been versatile experimental studies on quantum ground state physics, finite temperature thermal equilibrium, and quantum many-body dynamics, in fermionic quantum simulation systems. Quantum simulation offers an access to the physical problems that are intractable on the classical computer, including studying macroscopic quantum phenomena and microscopic physical mechanisms, which demonstrates the quantum advantages of controllable quantum systems. This paper briefly introduces the model of interacting fermions describing the quantum states of matter in such a system. Then we discuss various states of matter, which can arise in interacting fermionic quantum systems, including Cooper pair superfluids and density-wave orders. These exotic quantum states play important roles in describing high-temperature superconductivity and quantum magnetism, but their simulations on the classical computers have exponentially computational cost. Related researches on quantum simulation of interacting fermions in determining the phase diagrams and equation of states reflect the quantum advantage of such systems.

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Dissertations / Theses on the topic "Standard Equilibrium Quantum Systems"

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Kasztelan, Christian. "Strongly Interacting Quantum Systems out of Equilibrium." Diss., lmu, 2010. http://nbn-resolving.de/urn:nbn:de:bvb:19-124827.

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Lukkarinen, Jani. "Statistical analysis of finite equilibrium quantum systems." Helsinki : University of Helsinki, 2001. http://ethesis.helsinki.fi/julkaisut/mat/fysii/vk/lukkarinen/statisti.pdf.

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Dorner, Ross. "Non-equilibrium thermodynamics and dynamics of quantum systems." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/23916.

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This thesis is a study of non-equilibrium phenomena in quantum systems. Emphasis is given to the recently derived non-equilibrium fluctuation theorems, which relate the non-equilibrium response of a system to its equilibrium thermodynamic properties. We investigate the validity and importance of these theorems, from both a theoretical and experimental perspective, in systems ranging from a single atom to an ensemble of interacting particles. We also investigate the potential role of quantum dynamics in biological processes.

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Deesuwan, Tanapat. "Towards thermodynamics of quantum systems away from equilibrium." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/43379.

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A probability distribution encodes all the statistics of its corresponding random variable, hence it encodes all one can learn about the system via the random variable. In the theoretical part of this thesis, we discuss several equivalent representations of probability distributions in physics which establishes their roles as complete information measures in their own contexts. In particular, we show how Rényi entropies (as well as relative Rényi entropies) completely characterise the uncertainty of a system, hence implies the insufficiency of Shannon entropy (as well as relative entropy) in capturing the information in the presence of strong fluctuation. We also generalise Jarzynski equality in terms of relative Rényi entropies and show the equivalence between the generalised equality and the work distribution. As a consequence, an equivalence between a monotonic property of relative Rényi entropies and a kind of second law relations is revealed. In the experimental part, we study the non-equilibrium dynamics of an optically levitated nanosphere system in Knudsen regime and discover that, even though the system is not in equilibrium, the dynamics can still be treated as a Brownian motion with an effective temperature and an effective coefficient. Due to the Gaussian statistics of the levitated sphere, we show how some relevant non-equilibrium properties of the system, including several local temperatures, can be analysed from its power spectrum.

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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 thermoélectriques
This 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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MARCANTONI, STEFANO. "On the non-equilibrium thermodynamics of quantum systems." Doctoral thesis, Università degli Studi di Trieste, 2018. http://hdl.handle.net/11368/2917551.

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A consistent theory of non-equilibrium thermodynamics for Markovian open quantum systems has been developed in the late seventies in analogy with Classical Irreversible Thermodynamics. The time-evolution of these open systems is usually described by means of effective master equations in Lindblad form, that turn out to be reliable when there is a separation of time-scales between system and environment, such that memory effects are negligible and the so-called Markovian approximation is justified. In this framework, the variations of energy and entropy in the system are consistently described, distinguishing between heat and work contributions and providing a statement of the second law of thermodynamics as positivity of the entropy production. However, there is empirical evidence that many physical systems like photosynthetic complexes, opto-mechanical resonators and superconducting qubits, just to mention a few, experience more general non-Markovian dynamics. The formulation of the laws of thermodynamics in a non-Markovian setting is matter of current research and represents the main topic of the present work. As a first step, we show that the entropy production defined as in the Markovian case can be negative for a class of non-Markovian dynamics. We argue that this outcome should not be interpreted as a violation of the second law of thermodynamics because the environment must be explicitly taken into account in the balance of entropy in the non-Markovian setting. In order to justify this claim we adopt a more general point of view, studying a closed bipartite quantum system, such that each of the two subsystems plays the role of a finite environment out of equilibrium for the other one. We concentrate on the balance of energy first and construct an effective Hamiltonian for each subsystem using physically reasonable requirements; then we define heat and work as in the standard Markovian treatment, with the effective Hamiltonian replacing the free Hamiltonian. It turns out that, in our framework, the work power is perfectly balanced between subsystems, while the correlations can store a part of energy locally inaccessible and exchange it with both subsystems in the form of heat. Concerning the balance of entropy, a quite general formulation of the second law of thermodynamics can be given as follows: under the assumption of a factorized initial state for the compound system, the sum of the total variations of the entropies in the two subsystems is always nonnegative. We show with an explicit example that this general formulation does not correspond to the statement presented in the framework of Markovian master equations, which should not be considered a priori the second law of thermodynamics. In the last part of the thesis we concentrate of the so-called fluctuation relations, that are results extending the thermodynamic formalism beyond the behavior of average quantities. After reviewing the main theoretical outcomes, such as the Jarzynski equality and the Crooks fluctuation theorem, we describe a proposal to access experimentally the work performed on an ensemble of diatomic molecules by a time-dependent electric field coupled with their vibrational degree of freedom. This procedure could then be used to test the quantum Jarzynski equality. With respect to the results so far appeared in the literature, in which the left-hand side of the equality is inferred from an experiment and the right-hand side is computed according to a model, in our proposed setting we should be able to estimate from the experiment both the left-hand side and the right-hand side of the equality, independently.

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Holladay, Robert Tyler. "Steepest-Entropy-Ascent Quantum Thermodynamic Modeling of Quantum Information and Quantum Computing Systems." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/94630.

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Quantum information and quantum computing (QIQC) systems, relying on the phenomena of superposition and entanglement, offer the potential for vast improvements in certain computations. A practical QC realization requires maintaining the stored information for time-scales long enough to implement algorithms. One primary cause of information loss is decoherence, i.e., the loss of coherence between two energy levels in a quantum system. This work attributes decoherence to dissipation occurring as the system evolves and uses steepest-entropy-ascent quantum thermodynamics (SEAQT) to predict the evolution of system state. SEAQT asserts that, at any instant of time, the system state evolves such that the rate of system entropy change is maximized while conserving system energy. With this principle, the SEAQT equation of motion is applicable to systems in any state, near or far from stable equilibrium, making SEAQT particularly well suited for predicting the dissipation occurring as quantum algorithms are implemented. In the present research, the dynamics of qubits (quantum-bits) using the SEAQT framework are first examined during common quantum gates (combinations of which form algorithms). This is then extended to modeling a system of multiple qubits implementing Shor's algorithm on a nuclear-magnetic-resonance (NMR) QC. Additionally, the SEAQT framework is used to predict experimentally observed dissipation occurring in a two-qubit NMR QC undergoing a so called ``quenching'' process. In addition, several methods for perturbing the density or so-called ``state'' operator used by the SEAQT equation of motion subject to an arbitrary set of expectation value constraints are presented. These are then used as the basis for randomly generating states used in analyzing the dynamics of entangled, non-interacting systems within SEAQT. Finally, a reservoir interaction model is developed for general quantum systems where each system locally experiences a heat interaction with an external reservoir. This model is then used as the basis for developing a decoherence control scheme, which effectively transfers entropy out of the QIQC system as it is generated, thus, reducing the decoherence. Reservoir interactions are modeled for single qubits and the control scheme is employed in modeling an NMR QC and shown to eliminate nearly all of the noise caused by decoherence/dissipation.
Doctor of Philosophy
Quantum computers (QCs) have the potential to perform certain tasks much more efficiently than today0 s supercomputers. One primary challenge in realizing a practical QC is maintaining the stored information, the loss of which is known as decoherence. This work attributes decoherence to dissipation (a classical analogue being heat generated due to friction) occurring while an algorithm is run on the QC. Standard quantum modeling approaches assume that for any dissipation to occur, the QC must interact with its environment. However, in this work, steepest-entropy-ascent quantum thermodynamics (SEAQT) is used to model the evolution of the QC as it runs an algorithm. SEAQT, developed by Hatsopolous, Gyftopolous, Beretta, and others over the past 40 years, supplements the laws of quantum mechanics with those of thermodynamics and in contrast to the standard quantum approaches does not require the presence of an environment to account for the dissipation which occurs. This work first applies the SEAQT framework to modeling single qubits (quantum bits) to characterize the effect of dissipation on the information stored on the qubit. This is later extended to a nuclear-magnetic-resonance (NMR) QC of 7 qubits. Additionally, SEAQT is used to predict experimentally observed dissipation in a two-qubit NMR QC. Afterwards, several methods for constrained perturbations of a QC0 s state are presented. These methods are then used with SEAQT to analyze the effect of dissipation on the entanglement of two qubits. Finally, a model is derived within the SEAQT framework accounting for a qubit interacting with its environment, which is at a constant temperature. This model is then used to develop a method for limiting the decoherence and shown to significantly lowering the resulting error due to decoherence.

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Scopa, Stefano. "Non-equilibrium dynamics of driven low-dimensional quantum systems." Thesis, Université de Lorraine, 2019. http://www.theses.fr/2019LORR0084/document.

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Cette thèse analyse certains aspects de la dynamique hors équilibre de systèmes quantiques unidimensionnels lorsqu’ils sont soumis à des champs externes dépendant du temps. Nous considérons plus particulièrement le cas des forçages périodiques, et le cas d’une variation temporelle lente d’un paramètre de l’Hamiltonien qui permet de traverser une transition de phase quantique. La première partie contient une présentation des notions, des modèles et des outils nécessaires pour comprendre la suite de la thèse, avec notamment des rappels sur les modèles quantiques critiques (en particulier sur les chaines de spin et sur le modèle de Bose-Hubbard), le mécanisme de Kibble-Zurek, et la théorie de Floquet. Ensuite, nous étudions la dynamique hors équilibre des gaz de Tonks-Girardeau dans un potentiel harmonique dépendant du temps par différentes techniques : développements perturbatifs, diagonalisation numérique exacte et solutions analytiques exactes basées sur la théorie des invariants dynamiques d’Ermakov-Lewis. Enfin, nous analysons la dynamique hors équilibre des systèmes quantiques ouverts markoviens soumis à des variations périodiques des paramètres du système et de l’environnement. Nous formulons une théorie de Floquet afin d’obtenir des solutions exactes des équations de Lindblad périodiques. Ce formalisme de Lindblad-Floquet est utilisé pour obtenir une caractérisation exacte du fonctionnement en temps fini des machines thermiques quantiques
This thesis analyzes some aspects regarding the dynamics of one-dimensional quantum systems which are driven out-of-equilibrium by the presence of time- dependent external fields. Among the possible kinds of driven systems, our focus is dedicated to the slow variation of a Hamiltonian’s parameter across a quantum phase transition and to the case of a time-periodic forcing. To begin with, we prepare the background and the tools needed in the following. This includes a brief introduction to quantum critical models (in particular to the xy spin chain and to the Bose-Hubbard model), the Kibble-Zurek mechanism and Floquet theory. Next, we consider the non-equilibrium dynamics of Tonks-Girardeau gases in time-dependent harmonic trap potentials. The analysis is made with different techniques: perturbative expansions, numerical exact diagonalization and exact methods based on the theory of Ermakov-Lewis dynamical invariants. The last part of the thesis deals instead with the non-equilibrium dynamics of markovian open quantum systems subject to time-periodic perturbations of the system parameters and of the environment. This has led to an exact formulation of Floquet theory for a Lindblad dynamics. Moreover, within the Lindblad-Floquet framework it is possible to have an exact characterization ofthe finite-time operation of quantum heat-engines

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PORTA, SERGIO. "Non-equilibrium control of quantum systems and their phases." Doctoral thesis, Università degli studi di Genova, 2019. http://hdl.handle.net/11567/987246.

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In the last years, one of the major aim of the condensed matter area of interest, at the same rate of fundamental research, is to produce new and substantial breakthrough innovations to be applied in the information technology world. Indeed, semiconductor-based devices have constantly improved their performances thanks to the ability of continually shrink the components inside chips. In this process, however, physical components cannot be reduced in size infinitely. All matter consists of atoms and, at the atomic level, particles behave according to the laws of quantum mechanics. With this respect, the control of quantum systems is becoming fundamental to go beyond the present technology and the engineering of powerful phases of matter, very hard to obtain in standard conditions, is one of the main goals people are trying to achieve. The realization of quantum computation devices, in this sense, strongly depends on these new ideas success. In this respect, researchers have faced the difficulty, both from the theoretical and the experimental points of view, to control the state of a quantum system. Quantum control, i.e. the control of quantum phenomena, is becoming one of the major concerns in condensed matter physics, even if results obtained in the recent past are mainly confined to static systems in equilibrium, due to the difficulty to experimentally manipulate out-of-equilibrium quantum systems and the absence of an efficient general theoretical framework to describe non-equilibrium dynamics. In this thesis, I address these currently open questions by inspecting several different condensed matter models, using various methods to drive the system out of equilibrium and focusing on its dynamical features as well as the properties of its equilibration towards a thermal or, more interestingly, non thermal steady state. I discuss the possibility to manipulate various systems to give rise to peculiar dynamical behaviors and corresponding steady states with properties not attainable in thermal equilibrium, ranging from quantum phase transitions and their dynamical counterparts to superconductivity.

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Books on the topic "Standard Equilibrium Quantum Systems"

1

Schaller, Gernot. Open Quantum Systems Far from Equilibrium. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-03877-3.

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Schaller, Gernot. Open quantum systems far from equilibrium. Cham: Springer International Publishing, 2014.

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Kamenev, Alex. Field theory of non-equilibrium systems. Cambridge: Cambridge University Press, 2011.

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Suzuki, Masuo, ed. Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83154-6.

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Field theory of non-equilibrium systems. Cambridge: Cambridge University Press, 2011.

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Shastry, Abhay. Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-33574-8.

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Ingarden, Roman S. Information dynamics and open systems: Classical and quantum approach. Dordrecht: Kluwer, 1997.

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Algebraic aspects of Darboux transformations, quantum integrable systems, and supersymmetric quantum mechanics. Providence, R.I: American Mathematical Society, 2012.

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Taniguchi International Symposium on the Theory of Condensed Matter (9th 1986 Susono-shi, Japan). Quantum Monte Carlo methods in equilibrium and nonequilibrium systems: Proceedings of the Ninth Taniguchi International Symposium, Susono, Japan, November 14-18, 1986. Edited by Suzuki M. 1937-. Berlin: Springer-Verlag, 1987.

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Suzuki, Masuo. Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems: Proceedings of the Ninth Taniguchi International Symposium, Susono, Japan, November 14-18, 1986. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987.

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Book chapters on the topic "Standard Equilibrium Quantum Systems"

1

Gemmer, J., M. Michel, and G. Mahler. "18 Equilibrium Properties of Model Systems." In Quantum Thermodynamics, 185–219. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-44513-5_18.

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Montangero, Simone. "Many-Body Quantum Systems at Equilibrium." In Introduction to Tensor Network Methods, 97–108. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01409-4_7.

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Langen, Tim. "Isolated Quantum Systems Out of Equilibrium." In Springer Theses, 67–74. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18564-4_3.

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Bru, Jean-Bernard, and Walter de Alberto Siqueira Pedra. "Thermodynamic Equilibrium of Finite Quantum Systems." In C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics, 45–65. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-28949-1_3.

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Kraeft, Wolf-Dietrich, Dietrich Kremp, Werner Ebeling, and Gerd Röpke. "Quantum Statistical Calculations of Equilibrium Properties." In Quantum Statistics of Charged Particle Systems, 170–231. Boston, MA: Springer US, 1986. http://dx.doi.org/10.1007/978-1-4613-2159-0_6.

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Ashida, Yuto. "Out-of-Equilibrium Quantum Dynamics." In Quantum Many-Body Physics in Open Systems: Measurement and Strong Correlations, 87–143. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2580-3_4.

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Balzer, Karsten, and Michael Bonitz. "Quantum Many-Particle Systems out of Equilibrium." In Nonequilibrium Green's Functions Approach to Inhomogeneous Systems, 3–11. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35082-5_1.

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Kraeft, Wolf-Dietrich, Dietrich Kremp, Werner Ebeling, and Gerd Röpke. "Equilibrium Properties in Classical and Quasiclassical Approximation." In Quantum Statistics of Charged Particle Systems, 150–69. Boston, MA: Springer US, 1986. http://dx.doi.org/10.1007/978-1-4613-2159-0_5.

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Gerisch, Thomas. "Equilibrium States of Long Range Interacting Quantum Lattice Systems." In Large-Scale Molecular Systems, 351–56. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4684-5940-1_22.

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Betsuyaku, H. "Quantum Transfer-Matrix Method and Its Application to Quantum Spin Systems." In Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, 50–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83154-6_5.

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Conference papers on the topic "Standard Equilibrium Quantum Systems"

1

Briegel, Hans. "Entanglement in quantum many-body systems far away from thermodynamic equilibrium." In Workshop on Entanglement and Quantum Decoherence. Washington, D.C.: Optica Publishing Group, 2008. http://dx.doi.org/10.1364/weqd.2008.eoqs1.

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We show that quantum mechanical entanglement can prevail even in noisy open quantum many-body systems at high temperature and far away from thermodynamical equilibrium, despite the deteriorating effect of decoherence. The system consists of a number N of interacting quantum particles, and it can interact and exchange particles with some environment. The effect of decoherence is counteracted by a simple mechanism, where system particles are randomly reset to some standard initial state, e.g. by replacing them with particles from the environment.

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2

Moss, D. J., and T. Ido. "Calculation of photogenerated carrier escape rates from single GaAs / AlxGa1-xAs quantum wells." In International Conference on Ultrafast Phenomena. Washington, D.C.: Optica Publishing Group, 1994. http://dx.doi.org/10.1364/up.1994.md.21.

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There has been intense interest in the past few years in photogenerated carrier escape mechanisms from quantum wells1. This process is not only fundamental to understanding carrier dynamics in quantum confined systems, but has direct relevance to speed and intensity saturation limits for quantum well waveguide photodetectors and electroabsorption modulators2, reverse biased laser structures3, and optical SEED devices4. Only recently1, however, have escape times for both electrons and holes from single quantum wells been simultaneously and unambiguously measured with sub-picosecond resolution, and the results appeared to contradict simple existing theories for escape rates based on thermionic emission5 and tunneling. In this paper, we directly compare the results of our theory for photogenerated carrier escape rates as a function of applied field from single GaAs/AlGaAs quantum wells, with the experimental results from [1]; that is, for wells with x=0.2 and x=0.4 barriers at room temperature. We include thermionic emission (and for electrons include the effects of indirect conduction band minima in the well), thermally assisted, and direct tunneling. Our expressions for thermionic emission reduce, in the limit of large well width, to those5 which assume a 3D density of states. We assume that carriers in the well are in thermal equilibrium with each other and with the lattice, so “thermally assisted tunneling” refers here to tunneling from thermally occupied upper sub-bands - the 2D equivalent of Fowler-Nordheim tunneling. We also assume parabolic bands for holes within the quantum well, accounting for light / heavy hole mixing by using effective in-plane masses taken from the literature. Tunneling lifetimes are calculated using a standard6 transfer matrix approach to obtain the linewidths and energy levels of the quasi-bound states as a function of applied field. Under these assumptions the thermionic emission rate for electrons is

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3

SUZUKI, MASUO. "ON DISSIPATIVE QUANTUM DYNAMICS IN SMALL NON-EQUILIBRIUM SYSTEMS." In Quantum Bio-Informatics — From Quantum Information to Bio-Informatics. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812793171_0020.

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Jona-Lasinio, Giovanni. "On the statistics of quantum expectations for systems in thermal equilibrium." In QUANTUM MECHANICS: Are There Quantum Jumps? - and On the Present Status of Quantum Mechanics. AIP, 2006. http://dx.doi.org/10.1063/1.2219363.

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LIVERANI, CARLANGELO. "RETURN TO EQUILIBRIUM IN CLASSICAL AND QUANTUM SYSTEMS." In Proceedings of the Bologna APTEX International Conference. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812794598_0001.

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OJIMA, IZUMI. "NON-EQUILIBRIUM LOCAL STATES IN RELATIVISTIC QUANTUM FIELD THEORY." In Proceedings of the Japan-Italy Joint Workshop on Quantum Open Systems, Quantum Chaos and Quantum Measurement. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704412_0003.

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ARIMITSU, TOSHIHICO. "QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS IN VIEW OF NON-EQUILIBRIUM THERMO FIELD DYNAMICS." In Proceedings of the Japan-Italy Joint Workshop on Quantum Open Systems, Quantum Chaos and Quantum Measurement. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704412_0002.

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Goldstein, Sheldon, and Roderich Tumulka. "On the approach to thermal equilibrium of macroscopic quantum systems." In NONEQUILIBRIUM STATISTICAL PHYSICS TODAY: Proceedings of the 11th Granada Seminar on Computational and Statistical Physics. AIP, 2011. http://dx.doi.org/10.1063/1.3569494.

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Musho, T. D., S. M. Claiborne, and D. G. Walker. "NEGF Quantum Simulation of Field Emission Devices." In ASME/JSME 2011 8th Thermal Engineering Joint Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajtec2011-44504.

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Recent studies of wide band-gap diamond field emission devices have realized superior performance and lifetime. However, theoretical studies using standard Fowler-Nordheim (FN) theory do not fully capture the physics of diamond semiconductor emitters as a result of the fitting parameters inherent to the FN approximation. The following research computationally models wide band-gap field emission devices from a quantum point of view, using a novel non-equilibrium Green’s function (NEGF) approach previously applied to modeling solid-state electronic devices. Findings from this research confirm non-linearities in the FN curve and provide alternative explanations to discrepancies between standard FN theory.

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Haus, J. W., R. J. Glauber, W. Woger, and H. King. "Quantum Beat Superfluorescence." In Instabilities and Dynamics of Lasers and Nonlinear Optical Systems. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/idlnos.1985.wd24.

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That superfluorescence remains a fundamental cooperative phenomenon in quantum optics is attested to by the wealth of research publications and review articles on the subject1. Beyond the subfield of quantum optics, it is an important example of the decay of an unstable equilibrium state. Quantum fluctuations are necessary to trigger the decay of the atoms to the ground state; however, once begun the unstable nature of the process amplifies the tiny quantum fluctuations to macroscopic levels. Thus, superfluorescence gives us an insight into the nature of quantum stochastic processes.

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Reports on the topic "Standard Equilibrium Quantum Systems"

1

Zhu, Jianxin, and Benedikt Fauseweh. Digital quantum simulation of non-equilibrium quantum many-body systems. Office of Scientific and Technical Information (OSTI), May 2022. http://dx.doi.org/10.2172/1868210.

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DeMille, David, and Karyn LeHur. NON-EQUILIBRIUM DYNAMICS OF MANY-BODY QUANTUM SYSTEMS: FUNDAMENTALS AND NEW FRONTIER. Office of Scientific and Technical Information (OSTI), November 2013. http://dx.doi.org/10.2172/1108018.

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