Probing of quantum dissipative chaos by purity

TL;DR

This paper investigates how quantum purity can be used to identify and analyze chaotic dissipative dynamics in a nonlinear oscillator, revealing quantum effects linked to chaos through various driving regimes.

Contribution

It introduces a method to probe quantum chaos using purity, comparing quantum and classical indicators in a nonlinear dissipative oscillator system.

Findings

Purity reveals quantum signatures of chaos in NDO.

Chaotic regimes show distinct purity behavior compared to regular regimes.

Quantum effects related to chaos are elucidated under different driving conditions.

Abstract

In this paper, the purity of quantum states is applied to probe chaotic dissipative dynamics. To achieve this goal, a comparative analysis of regular and chaotic regimes of nonlinear dissipative oscillator (NDO) are performed on the base of excitation number and the purity of oscillatory states. While the chaotic regime is identified in our semiclassical approach by means of strange attractors in Poincar\'e section and with the Lyapunov exponent, the state in the quantum regime is treated via the Wigner function. Specifically, interesting quantum purity effects that accompany the chaotic dynamics are elucidated in this paper for NDO system driven by either: (i) a time-modulated field, or (ii) a sequence of pulses with Gaussian time-dependent envelopes.