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Entropy
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Quantum Nonequilibrium Dynamics
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Quantum Nonequilibrium Dynamics

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (30 June 2016) | Viewed by 25751

Special Issue Editor

Prof. Dr. Martin Eckstein

E-Mail Website
Guest Editor
Theory of Correlated Systems out of Equilibrium Group, Max Planck Research Department of Condensed Matter Dynamics, University of Hamburg, Luruper Chaussee 149, Geb. 99 (CFEL) 22761 Hamburg, Germany
Interests: theory of strongly correlated quantum systems in nonequilibrium; control of complex material properties by light; numerical approaches for the real-time dynamics of many-particle systems

Special Issue Information

Dear Colleagues

The nonequilibrium dynamics of quantum matter is currently being addressed along various frontiers in condensed matter physics, bridging from transport through molecules and quantum dots, to the light-control of complex materials, and all the way to the fundamental questions of statistical physics. Femtosecond laser pulses can trigger ultra-fast phase transitions, and allow the study of time-evolution of solids on timescales in which their microscopic constituents are not even locally in thermal equilibrium. Floquet-Hamiltonians can be designed by time-periodic driving under nonequilibrium conditions, to generate artificial gauge fields and topologically nontrivial band structures. Moreover, using cold atoms in optical lattices, one can address long-standing questions of nonequilibrium statistical physics: How does a many-body relax to thermal equilibrium? Does a system heat up indefinitely under external time-periodic driving, or does its energy eventually localize? Solving the quantum dynamics of many particles out of equilibrium still remains a challenge, but the intensive research of the previous years has lead to enormous progress in the development of numerical methods, including, without any claim of completeness, real-time quantum Monte Carlo, the time-dependent density matrix renormalization method, or time-dependent functional renormalization techniques. This Special Issue encourages physicists to contribute work on related questions, with the aim to give a broad picture of the current state of this rapidly evolving field of research.

Prof. Dr. Martin Eckstein
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

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Published Papers (3 papers)

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Research

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6766 KiB  
Article
Quantum Hysteresis in Coupled Light–Matter Systems
by Fernando J. Gómez-Ruiz, Oscar L. Acevedo, Luis Quiroga, Ferney J. Rodríguez and Neil F. Johnson
Entropy 2016, 18(9), 319; https://doi.org/10.3390/e18090319 - 7 Sep 2016
Cited by 8 | Viewed by 6047
Abstract
We investigate the non-equilibrium quantum dynamics of a canonical light–matter system—namely, the Dicke model—when the light–matter interaction is ramped up and down through a cycle across the quantum phase transition. Our calculations reveal a rich set of dynamical behaviors determined by the cycle [...] Read more.
We investigate the non-equilibrium quantum dynamics of a canonical light–matter system—namely, the Dicke model—when the light–matter interaction is ramped up and down through a cycle across the quantum phase transition. Our calculations reveal a rich set of dynamical behaviors determined by the cycle times, ranging from the slow, near adiabatic regime through to the fast, sudden quench regime. As the cycle time decreases, we uncover a crossover from an oscillatory exchange of quantum information between light and matter that approaches a reversible adiabatic process, to a dispersive regime that generates large values of light–matter entanglement. The phenomena uncovered in this work have implications in quantum control, quantum interferometry, as well as in quantum information theory. Full article
(This article belongs to the Special Issue Quantum Nonequilibrium Dynamics)
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955 KiB  
Article
Relationship between Population Dynamics and the Self-Energy in Driven Non-Equilibrium Systems
by Alexander F. Kemper and James K. Freericks
Entropy 2016, 18(5), 180; https://doi.org/10.3390/e18050180 - 13 May 2016
Cited by 10 | Viewed by 4702
Abstract
We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches must give the same answer, [...] Read more.
We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches must give the same answer, it is common to make a number of simplifying assumptions, within the differential equation for the populations, that allows one to interpret the decay in terms of hot electrons interacting with a phonon bath. Here, we show how care must be taken to ensure an accurate treatment of the equation of motion for the populations due to the fact that there are identities that require cancellations of terms that naively look like they contribute to the decay rates. In particular, the average time dependence of the Green’s functions and self-energies plays a pivotal role in determining these decay rates. Full article
(This article belongs to the Special Issue Quantum Nonequilibrium Dynamics)
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Review

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1755 KiB  
Review
Introduction to Supersymmetric Theory of Stochastics
by Igor V. Ovchinnikov
Entropy 2016, 18(4), 108; https://doi.org/10.3390/e18040108 - 28 Mar 2016
Cited by 31 | Viewed by 14444
Abstract
Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order’s omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and [...] Read more.
Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order’s omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and phenomenological frameworks, and experimental phenomena such as turbulence, 1/f noise, dynamical complexity, chaos and the butterfly effect, the Richter scale for earthquakes and the scale-free statistics of other sudden processes, self-organization and pattern formation, self-organized criticality, etc. Although several successful approaches to various realizations of DLRO have been established, the universal theoretical understanding of this phenomenon remained elusive. The possibility of constructing a unified theory of DLRO has emerged recently within the approximation-free supersymmetric theory of stochastics (STS). There, DLRO is the spontaneous breakdown of the topological or de Rahm supersymmetry that all stochastic differential equations (SDEs) possess. This theory may be interesting to researchers with very different backgrounds because the ubiquitous DLRO is a truly interdisciplinary entity. The STS is also an interdisciplinary construction. This theory is based on dynamical systems theory, cohomological field theories, the theory of pseudo-Hermitian operators, and the conventional theory of SDEs. Reviewing the literature on all these mathematical disciplines can be time consuming. As such, a concise and self-contained introduction to the STS, the goal of this paper, may be useful. Full article
(This article belongs to the Special Issue Quantum Nonequilibrium Dynamics)
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