Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation

TL;DR

This paper investigates how a quantum nonlinear pendulum transitions from order to chaos under noisy perturbations, revealing finite-time stability domains influence quantum dynamics and leave detectable patterns even in chaotic regimes.

Contribution

It introduces a novel analysis of finite-time stability effects on quantum chaos using the FTEO and Poincaré map techniques.

Findings

Finite-time stability domains create ordered patterns in FTEO eigenfunctions.

Transition to chaos causes these patterns to smear but some traces persist.

Finite-time stability influences quantum dynamics significantly.

Abstract

Motion of randomly-driven quantum nonlinear pendulum is considered. Utilizing one-step Poincar\'e map, we demonstrate that classical phase space corresponding to a single realization of the random perturbation involves domains of finite-time stability. Statistical analysis of the finite-time evolution operator (FTEO) is carried out in order to study influence of finite-time stability on quantum dynamics. It is shown that domains of finite-time stability give rise to ordered patterns in distributions of FTEO eigenfunctions. Transition to global chaos is accompanied by smearing of these patterns; however, some of their traces survive on relatively long timescales.