Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Role of parametric noise in nonintegrable quantum dynamics

Rainer Scharf, Bala Sundaram

Published Apr 1, 1994• 3 citations

Abstract

The effect of parametric perturbations on the quantum dynamics of a system with nonintegrable classical limit and a mixed phase space is shown to depend crucially on the local invariant phase space structures sampled by the evolution. Using a probe coherent state four distinct scenarios are considered: (i) large regular regions surrounding primary fixed points; (ii) smaller regular regions corresponding to higher order orbits; (iii) scarred states on hyperbolic fixed points; (iv) chaotic regions. The result that scarring stabilizes quantum dynamics against fluctuations is discussed in the general context of instability in the quantum evolution as well as in relation to recent experiments on microwave ionization of Rydberg atoms.

DOI: 10.1103/physreve.49.r2509

Related papers

Phase Space Structures in Chaotic Quantum Dynamics.

B. S. Helmkamp

I compare the quantum and classical dynamics of a particle moving in a cosine potential while subject to a time-dependent force. I concentrate here on the behavior of an initially well-localized wave packet at times before the classically chaotic motion is fully developed. I find that the quantum and classical dynamics are indistinguishable well beyond the Ehrenfest time where the wave packet delocalizes. The quantum and classical descriptions first differ precisely when the classical probability density is folded in the vicinity of a hyperbolic fixed point. At this point, the wave function acquires a nodal structure which I show to be the result of a simple beating phenomenon between paths in the semiclassical propagator. When the interaction of the classical manifold with the hyperbolic fixed point leads to escape from the remnant separatrix, representing the onset of classical chaos, the interference associated with the tendril leads to a long-lived accumulation of quantum amplitude on top of the cosine barrier. This effect also has a semiclassical interpretation, meaning that it arises from the interference between classical paths, but one must expand to second order in Planck's constant to describe the behavior correctly. Both the nodal structure and this pinning of amplitude on the barrier are dynamic mechanisms for the quantum inhibition of mixing. I then couple the system to a bath of harmonic oscillators in order to study the effect of the environment on these mechanisms. Although an oscillator bath environment brings dissipation as well as noise to the problem, the noise effect dominates for the high temperature, weak coupling regime I study. When there is sufficient noise to render the interfering classical paths indistinguishable, I find that the quantum interference gets erased. This dephasing occurs at very early times, long before there is appreciable dissipation of energy to the environment. Consequently, one can argue that the presence of an environment, even if its effect would be negligible in a nonchaotic setting, allows for the possibility of quantum mixing.

Civil War Book ReviewJan 1, 19950 citations

Coherence And Chaos In A Quantum Optical System

Gerard J Milburn

The quantum dynamics of periodically kicked hamiltonian systems can reflect the classical dynamics be it regular or chaotic. However in quantum systems the classical chaotic diffusion of one phase space variable is suppressed due to irregular recurrences in the quantum state. This aspect of quantum nonlinear dynamics should be accessible to experimental test and recent results on the microwave ionization of hydrogen would seem to confirm it.

Digest on Nonlinear Optics: Materials, Phenomena and DevicesJan 1, 19901 citation

Semiclassics of the chaotic quantum-classical transition

Benjamin D. Greenbaum, Salman Habib, Kosuke Shizume +1 more

We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the dual role of noise in regularizing the semiclassical Wigner function and averaging over fine structures in classical phase space. The results are interpreted in the context of applying recent advances in the theory of measurement and open systems to the semiclassical quantum regime. We use these methods to show how a local semiclassical picture is stabilized and can then be approximated by a classical distribution at later times. The general results are demonstrated explicitly via high-resolution numerical simulations of the quantum master equation for a chaotic Duffing oscillator.

arXiv:quant-ph/0610004Physical Review EOct 18, 200721 citations

Fingerprints of classical instability in open quantum dynamics

Paul Miller, Sarben Sarkar

The dynamics near a hyperbolic fixed point in phase space is modeled by an inverted harmonic oscillator. We investigate the effect of the classical instability on the open quantum dynamics of the oscillator, introduced through the interaction with a thermal bath, using both the survival probability function and the rate of von Neumann entropy increase, for large times. In this parameter range we prove, using influence functional techniques, that the survival probability function decreases exponentially at a rate ${\ensuremath{\kappa}}^{\ensuremath{'}}$ depending not only on the measure of instability in the model but also on the strength of interaction with the environment. We also show that ${\ensuremath{\kappa}}^{\ensuremath{'}}$ determines the rate of the von Neumann entropy increase and that this result is independent of the temperature of the environment. This generalizes earlier results that are valid in the limit of vanishing dissipation. The validity of inferring similar rates of survival probability decrease and entropy increase for quantum chaotic systems is also discussed.

arXiv:chao-dyn/9807009Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsOct 1, 199833 citations

A driven two-component BEC: Chaos in a Macroscopic Quantum System

Jiří Tomkovič

This work discusses the experimental realization of a mixed regular-chaotic phase space in a macroscopic quantum system. The effective Planck's constant of the system can be varied in a large range. Therefore, the semi-classical limit of the system can be studied, where the initial size of the many particle wave packet is much smaller than typical structures of the phase space. Thus, different structures of the phase space can be resolved. In a weakly driven system, the Poincaré-Birkhoff scenario is investigated by the dispersion of the wave packet at a stable or unstable fixed point. In a strongly driven system, different dynamics of a wave packet is found, dependent on preparation in a regular island or the chaotic sea. The time evolution can be described by a classical model, which is in good agreement with experiment as well as the mean field model for the considered observables. \n \nIn an independent experiment using an atomic beam setup the generation of motional coherence of a single atom by spontaneous emission of a single photon has been demonstrated.

Jan 1, 20140 citations

Slow quantum thermalization and many-body revivals from mixed phase space

Michailidis, AA, Turner, CJ, Zlatko Papić +2 more

The relaxation of few-body quantum systems can strongly depend on the initial state when the system’s semiclassical phase space is mixed; i.e., regions of chaotic motion coexist with regular islands. In recent years, there has been much effort to understand the process of thermalization in strongly interacting quantum systems that often lack an obvious semiclassical limit. The time-dependent variational principle (TDVP) allows one to systematically derive an effective classical (nonlinear) dynamical system by projecting unitary many-body dynamics onto a manifold of weakly entangled variational states. We demonstrate that such dynamical systems generally possess mixed phase space. When TDVP errors are small, the mixed phase space leaves a footprint on the exact dynamics of the quantum model. For example, when the system is initialized in a state belonging to a stable periodic orbit or the surrounding regular region, it exhibits persistent many-body quantum revivals. As a proof of principle, we identify new types of “quantum many-body scars,” i.e., initial states that lead to long-time oscillations in a model of interacting Rydberg atoms in one and two dimensions. Intriguingly, the initial states that give rise to most robust revivals are typically entangled states. On the other hand, even when TDVP errors are large, as in the thermalizing tilted-field Ising model, initializing the system in a regular region of phase space leads to a surprising slowdown of thermalization. Our work establishes TDVP as a method for identifying interacting quantum systems with anomalous dynamics in arbitrary dimensions. Moreover, the mixed phase space classical variational equations allow one to find slowly thermalizing initial conditions in interacting models. Our results shed light on a link between classical and quantum chaos, pointing toward possible extensions of the classical Kolmogorov-Arnold-Moser theorem to quantum systems.

Mar 4, 202087 citations