Dynamical Stability in a Non-Hermitian Kicked Rotor Model

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.

Automated summary

We investigate the quantum irreversibility and quantum diffusion in a non-Hermitian kicked rotor model with complex kicking strength. The results show that increasing the strength of the imaginary part of the non-Hermitian potential suppresses the exponential decay of the Loschmidt echo and enhances dynamical localization. Quantum diffusion exhibits dynamical localization in momentum space, and the mean square of momentum increases to saturation with time evolution but decreases with the increase of the imaginary part of the kicking strength. The quantum state is mainly populated on a few quasieigenstates with a large imaginary part of quasienergies, and the stability of wavepacket's dynamics and the dynamical localization of energy diffusion are determined by the feature of quasieigenstates.