Abstract
The motion of a randomly driven quantum nonlinear pendulum is considered. Utilizing a one-step Poincaré map, we demonstrate that the classical phase space corresponding to a single realization of the random perturbation can involve domains of finite-time stability. Statistical analysis of the finite-time evolution operator (FTEO) is carried out in order to study the 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. The transition to global chaos is accompanied by smearing of these patterns; however, some of their traces survive on relatively long timescales.
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