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Journal of Statistical Mechanics Theory and Experiment

Exactly soluble quantum model for repeated harmonic perturbation

Hiroshi Tamura, Valentin Anatol'evich Zagrebnov

Published Oct 9, 2015• 3 citations
Publisher

Abstract

We consider an exactly soluble dynamical system with inelastic repeated harmonic perturbation. Hamiltonian dynamics is quasi-free, and it leads in the large-time limit to relaxation of initial states and to entropy production. To study correlations we consider the time evolution of subsystems. We prove a universality of dynamics driven by repeated harmonic perturbation in a short-time interaction limit.

DOI
10.1088/1742-5468/2015/10/p10005

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We consider an exactly soluble dynamical system with inelastic repeated harmonic perturbation. Hamiltonian dynamics is quasi-free, and it leads in the large-time limit to relaxation of initial states and to entropy production. To study correlations we consider the time evolution of subsystems. We prove a universality of dynamics driven by repeated harmonic perturbation in a short-time interaction limit.
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We consider an exactly solvable model of nonautonomous W *-dynamics driven by repeated harmonic interaction. The dynamics is Hamiltonian and quasifree. Because of inelastic interaction in the large-time limit, it leads to relaxation of initial states to steady states. We derive the explicit entropy production rate accompanying this relaxation. We also study the evolution of different subsystems to elucidate their eventual correlations and convergence to equilibriums. In conclusion, we prove that the W *-dynamics manifests a universal stationary behavior in a short-time interaction limit.
In the framework of an exactly soluble model, one considers a typical problem of the interaction between radiation and matter: the dynamics of population in a multilevel quantum system subject to a time dependent perturbation. The algebraic structure of the model is taken richly enough, such that there exists a strong argument in favor of the fact that the behavior of the system in the asymptotic of long time has a universal character, which is system-independent and governed by the functional property of the time dependence exclusively. Functional properties of the excitation time dependence, resulting in the regimes of resonant excitation, random walks, and dynamic localization, are identified. Moreover, an intermediate regime between the random walks and the localization is identified for the polyharmonic excitation at frequencies given by the Liouville numbers.
Entropy production provides a general way to state the second law of thermodynamics for nonequilibrium scenarios.In open quantum system dynamics, it also serves as a useful quantifier of the degree of irreversibility.In this work we shed light on the relation between correlations, initial preparation of the system, and non-Markovianity by studying a system of two harmonic oscillators independently interacting with their local baths.Their dynamics, described by a time-local master equation, is solved to show, both numerically and analytically, that the global purity of the initial state of the system influences the behavior of the entropy production rate and that the latter depends algebraically on the entanglement that characterizes the initial state.
The quantum dynamics of isolated systems under quench condition exhibits a variety of interesting features depending on the integrable/chaotic nature of system. We study the exact dynamics of trivially integrable system of harmonic chains under a multiple quench protocol. Out of time ordered correlator of two Hermitian operators at large time displays scrambling in the thermodynamic limit. In this limit, the entanglement entropy and the central component of momentum distribution both saturate to a steady-state value. We also show that reduced density matrix assumes the diagonal form long after multiple quenches for large system size. These exact results involving infinite-dimensional Hilbert space are indicative of dynamical equilibration for a trivially integrable harmonic chain.
Abstract It is a fundamental problem to characterize nonequilibrium processes. For a moving one-dimensional potential, we explore the nonequilibrium dynamics of the initial energy eigenstates for a confined quantum system interacting with a large reservoir. For concreteness, we investigate a dragged harmonic oscillator linearly interacting with an assembly of harmonic oscillators, and explore the deviation from adiabatic processes by rigorously calculating the so-called persistent amplitude. In particular, we show that the phase of the persistent amplitude is considered to be common both for the ground and excited states. Also, we can define the quasi adiabatic processes in a well-defined double limit of small perturbation and a sufficiently long time in terms of the phase and absolute value of the persistent amplitude.