In a PT-symmetric kicked harmonic oscillator, non-resonant driving yields directed momentum current with ballistic energy growth, while resonant driving yields damped cosine oscillations of momentum and energy with a common frequency.
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Ballistic diffusion vs. damped oscillation of energy in a $\mathcal{PT}$-symmetric quantum kicked harmonic oscillator
In a PT-symmetric kicked harmonic oscillator, non-resonant driving yields directed momentum current with ballistic energy growth, while resonant driving yields damped cosine oscillations of momentum and energy with a common frequency.