Limit of classical chaos in quantum systems

Physical Review A, 2012

We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude-a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.

1996

Physica A: Statistical Mechanics and its Applications, 1990

The localization phenomenon plays an essential role in the excitation of hydrogen atoms in microwave fields. The similarity of this phenomenon to Anderson localization, which has been established and discussed in previous papers, is here demonstrated in a transparent way by reducing the quantum dynamics to a one-dimensional pseudo-Anderson model. The effect of slight changes in the driving frequency on the ionization probability is numerically investigated on the quantum Kepler map; huge fluctuations are found, which persist down to a very fine frequency scale and have a qualitatively random nature. It is argued that such fluctuations are a counterpart of the mesoscopic fluctuations of solid-state physics, and that similar fluctuations should be expected any time, when some classical chaotic diffusive process is quantum-mechanically suppressed by dynamical localization.

The Journal of Physical Chemistry, 1982

in an MCSCF wave function to assure it is a reasonable representation of a state of the system. For the nth state of a certain symmetry, these include the following: (i) the full Hessian has n-1 negative eigenvalues, (ii) the MCTDHF is stable and has n-1 negative excitation energies, (iii) the state is the nth state in energy of a CI with MCSCF configurations. Ideally, all of these criteria should be fulfilled. However, there are cases where one or more of these are not fulfilled, e.g., near avoided curve crossings. Also new calculational results for the 21A1 state in CH2 and the second lZg+ state of Cz have been presented. Generalizations of Newton-Raphson and multiplicity independent Newton-Raphson procedures are presented and analyzed. We have shown how quadratic, cubic, quartic, ... convergence may be obtained with fixed Hessian-type approaches. Sample calculations are presented for convergence to the E3Z,state of 02.

Physics Letters A, 1991

Scale transformations for the classical and quantum dynamics of the hydrogen atom in a harmonic field are introduced which reduce the number of parameters, simplify the analysis of the chaotic dynamics and reveal the functional dependences of the classical and quantum processes.

2002

We use the quantum action to study the dynamics of quantum system at finite temperature. We construct the quantum action non-perturbatively and find temperature dependent action parameters. Here we apply the quantum action to study quantum chaos. We present a numerical study of a classically chaotic 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling. We compare Poincar\'e sections for the quantum action at finite temperature with those of classical action.

1999

This thesis is concerned with the study, classically and quantum mechanically, of the square billiard with particular attention to chaos in both cases. Classically, we show that the rotating square billiard has two regular limits with a mixture of order and chaos between, depending on an energy parameter, E. This parameter ranges from -2a;^ to oo, where u is the angular rotation, corresponding to the two integrable limits. The rotating square billiard has simple enough geometry to permit us to elucidate that the mechanism for chaos with rotation or curved trajectories is not flyaway, as previously suggested, but rather the accumulation of angular dispersion from a rotating line. Furthermore, we find periodic cycles which have asymmetric trajectories, below the value of E at which phase space becomes disjointed. These trajectories exhibit both left and right hand curvatures due to the fine balance between Centrifugal and Coriolis forces. Quantum mechanically, we compare the spectral analysis results for the square billiard with three different theoretical distribution functions. A new feature in the study is the correspondence we find, by utilising the Berry-Robnik parameter q, between classical E and a quantum rotation parameter cu. The parameter q gives the ratio of chaotic quantum phase volume which we can link to the ratio of chaotic phase volume found classically for varying values of E. We find good correspondence, in particular, the different values of ^ as a; is varied refiect the births and subsequent destructions of the different periodic cycles. We also study wave packet dynamics, necessitating the adaptation of a one dimensional unitary integration method to the two dimensional square billiard. In concluding we suggest how this work may be used, with the aid of the chaotic phase volumes calculated, in future directions for research work. n Declaration

Nuclear Physics B, 1996

We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the form of a functional supermatrix nonlinear σ-model where the effective action involves the evolution operator of the classical dynamics. Low-lying degrees of freedom of the field theory are shown to reflect the irreversible classical dynamics describing relaxation of phase space distributions. The validity of this approach is investigated over a wide range of energy scales. As well as recovering the universal long-time behavior characteristic of random matrix ensembles, this approach accounts correctly for the short-time limit yielding results which agree with the diagonal approximation of periodic orbit theory.

Modern Optics and Photonics - Atoms and Structured Media - Proceedings of the International Advanced Research Workshop, 2010

We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions. For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with time-dependent Kerr-nonlinearity and time-modulated driving field. This model showing both regular and chaotic dynamics in the classical limit is realized in several experimental schemes. Quantum dissipative chaos is analyzed on the base of numerical method of quantum trajectories. Three quantities are studied: the Wigner function of oscillatory mode from the point of view of quantum-assemble theory and both semiclassical Poincaré section and quantum Poincaré section calculated on a single quantum trajectory. The comparatively analysis of these distributions for various operational chaotic regimes of the models is performed, as well as scaling invariance in dissipative chaos and quantum interference effects assisted by chaos are discussed.

An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -characteristic of all realistic dynamical systems -suppress the development of fine structure in classical phase space and damp nonlocal contributions to the semiclassical Wigner function which would otherwise invalidate the approximation. This dual regularization of the singular nature of the semiclassical limit is demonstrated by a numerical investigation of the chaotic Duffing oscillator.