Dynamical stability in a non-Hermitian kicked rotor model

TL;DR

This paper studies how non-Hermiticity affects quantum irreversibility and localization in a kicked rotor model, revealing suppression of exponential decay and enhancement of dynamical localization with increasing imaginary potential strength.

Contribution

It provides analytical and numerical insights into how non-Hermitian dynamics influence quantum stability and localization phenomena in kicked rotor systems.

Findings

Exponential decay of Loschmidt echo diminishes with increased non-Hermiticity.

Dynamical localization in momentum space is enhanced by non-Hermitian effects.

Quasieigenstates become more localized as the imaginary part of the potential increases.

Abstract

We investigate the quantum irreversibility and quantum diffusion in a non-Hermitian kicked rotor model for which the kicking strength is complex. Our results show that the exponential decay of Loschmidt echo gradually disappears with increasing the strength of the imaginary part of non-Hermitian driven potential, demonstrating the suppress of the exponential instability by non-Hermiticity. The quantum diffusion exhibits the dynamical localization in momentum space, namely, the mean square of momentum increases to saturation with time evolution, which decreases with the increase of the strength of the imaginary part of the kicking. This clearly reveals the enhancement of dynamical localization by non-Hermiticity. We find, both analytically and numerically, that the quantum state are mainly populated on a very few quasieigenstates with significantly large value of the imaginary part of quasienergies. Interestingly, the average value of the inverse participation ratio of quasieigenstates decreases with the increase of the strength of the imaginary part of the kicking potential, which implies that the feature of quasieigenstates determines the stability of wavepacket's dynamics and the dynamical localization of energy diffusion.