Ballistic diffusion vs. damped oscillation of energy in a $\mathcal{PT}$-symmetric quantum kicked harmonic oscillator

TL;DR

This paper investigates the quantum dynamics of a non-Hermitian, $ ext{PT}$-symmetric kicked harmonic oscillator, revealing coexistence of directed momentum current and ballistic energy diffusion, as well as damped oscillations under different conditions.

Contribution

It provides a numerical analysis of how non-Hermiticity influences energy and momentum behaviors in a $ ext{PT}$-symmetric quantum system, highlighting the mechanisms behind observed phenomena.

Findings

Directed momentum current and ballistic energy diffusion coexist under non-resonant conditions.

Momentum and energy oscillate as damped cosines with identical frequencies under resonant conditions.

Non-Hermiticity and system frequency jointly produce these dynamical behaviors.

Abstract

We numerically study the quantum dynamics of a $\mathcal{PT}$-symmetric kicked harmonic oscillator. We observe that directed current of momentum and ballistic diffusion of energy coexist under the non-resonant conditions, whereas both the momentum and energy oscillate as damped cosine functions with identical frequencies under the resonant conditions. The research shows that the directed current of momentum and ballistic diffusion of energy arise from nearest-neighbor hopping between momentum eigenstates with the non-Hermitian driving, while the damped oscillations of momentum and energy originate from resonant coupling between the non-Hermitian driving and the harmonic oscillator. Our findings indicate that the non-Hermiticity and the frequency characteristic of this system collectively result in these distinctive dynamical behaviors.