Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Introduction
- Part One Classical chaos and quantum localization
- Stochastic behaviour of a quantum pendulum under a periodic perturbation
- Quantum dynamics of a nonintegrable system
- Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization
- Localization of diffusive excitation in multi-level systems
- Classical and quantum chaos for a kicked top
- Self-similarity in quantum dynamics
- Time irreversibility of classically chaotic quantum dynamics
- Effect of noise on time-dependent quantum chaos
- Dynamical localization, dissipation and noise
- Maximum entropy models and quantum transmssion in disordered systems
- Solid state “atoms” in intense oscillating fields
- Part Two Atoms in strong fields
- Part Three Semiclassical approximations
- Part Four Level statistics and random matrix theory
- Index
Time irreversibility of classically chaotic quantum dynamics
Published online by Cambridge University Press: 07 May 2010
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Introduction
- Part One Classical chaos and quantum localization
- Stochastic behaviour of a quantum pendulum under a periodic perturbation
- Quantum dynamics of a nonintegrable system
- Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization
- Localization of diffusive excitation in multi-level systems
- Classical and quantum chaos for a kicked top
- Self-similarity in quantum dynamics
- Time irreversibility of classically chaotic quantum dynamics
- Effect of noise on time-dependent quantum chaos
- Dynamical localization, dissipation and noise
- Maximum entropy models and quantum transmssion in disordered systems
- Solid state “atoms” in intense oscillating fields
- Part Two Atoms in strong fields
- Part Three Semiclassical approximations
- Part Four Level statistics and random matrix theory
- Index
Summary
Abstract
The nature of classically chaotic quantum dynamics is studied by menas of a numerical time reversal experiment. It turns out that there is a fundamental quantum scale below which the system cannot exhibit classical irreversibility to external perturbations. On the other hand, a paradoxical phenomenon manifesting that quantum irreversibility may exceed its classical counterpart is discovered. These features are explained in terms of semicalssical dynamical theory.
Introduction
Classically chaotic quantum systems in general can exhibit intrinsinc chaotic behaviour on a quite restricted time scale [1], In particular localization phenomena provide direct evidence exhibiting the suppression of quantum ergodicity [2]. On the other hand, recent studies reveal that a many-dimensional system can mimic some aspects peculiar to chaotic dynamics quite well on an unexpectedly long time scale [3]. A remarkable feature that distinguishes chaotic motion from integrable motion is the sensitive dependence of dynamics on external perturbations. For classical dynamical systems such a sensitivity can be well defined by measuring how two nearby trajectories in the phase space separate in time. However, there has been proposed no systematic way to examine the sensitivity of quantum dynamics to external perturbation. In quantum dynamics, it is not possible to trace a well defined trajectory in phase space, because both quantum uncertainty and chaotic instability make a localized wavepacket spread suddenly over the phase space [4]. There is, however, a simple way in which we may test the quantum sensitivity quantitively. This is the time reversal experiment described below. In this chapter I describe several remarkable characteristics of quantal instability which have been clarified by the time reversal experiment.
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- Quantum ChaosBetween Order and Disorder, pp. 147 - 156Publisher: Cambridge University PressPrint publication year: 1995