Quantum Dynamics Against a Noisy Background

TL;DR

This paper studies how persistent external noise affects the dynamics, stability, and reversibility of a quantum chaotic system, specifically a kicked quartic oscillator, and identifies critical noise levels and decoherence times.

Contribution

It provides a detailed analysis of noise effects on quantum chaos, including the critical noise threshold and decoherence time, with new insights into stability and reversibility under noise influence.

Findings

Critical noise level $\sigma_c(t)$ depends on evolution time.

Power-like dependence of $\sigma_c(t)$ when Ehrenfest time is short.

Estimated decoherence time for transition to Markovian dynamics.

Abstract

By the example of a kicked quartic oscillator we investigate the dynamics of classically chaotic quantum systems with few degrees of freedom affected by persistent external noise. Stability and reversibility of the motion are analyzed in detail in dependence on the noise level $\sigma$. The critical level $\sigma_c(t)$, below which the response of the system to the noise remains weak, is studied versus the evolution time. In the regime with the Ehrenfest time interval $t_E$ so short that the classical Lyapunov exponential decay of the Peres fidelity does not show up the time dependence of this critical value is proved to be power-like. We estimate also the decoherence time after which the motion turns into a Markovian process.