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arXiv:2211.00831 · Physical Review A

Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors

Jian-Zheng Li, Wen-Lei Zhao, Jie Liu

Published Mar 13, 2023• 6 citations
arXivHTMLPDF

Abstract

We numerically investigate the quantum transport in coupled kicked rotors with $\mathcal{PT}$-symmetric potential. We find that spontaneous $\mathcal{PT}$-symmetry breaking of wave functions emerges when the amplitude of the imaginary part of the complex potential is beyond a threshold value, which can be modulated by the coupling strength effectively. In the regime of $\mathcal{PT}$-symmetry breaking, the particles driven by the periodical kicks move unidirectionally in momentum space, indicating the emergence of a directed current. Meanwhile, with increasing the coupling strength, we find a transition from the ballistic energy diffusion to a kind of modified ballistic energy diffusion where the width of the wave packet also increases with time in a power law. Our findings suggest that the decoherence effect induced by the interplay between the interparticle coupling and the non-Hermitian driving potential is responsible for these particular transport behaviors.

DOI
10.1103/physreva.107.032208

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Abstract We numerically study the quantum dynamics of a P T -symmetric kicked harmonic oscillator. The P T symmetry breaks spontaneously when the non-Hermitian driving strength surpasses the exceptional point. In the P T -broken phase, 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.
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We investigate the dynamics of the out-of-time-ordered correlators (OTOCs) via a non-Hermitian extension of the quantum kicked rotor model, where the kicking potential satisfies PT\mathcal{PT}PT-symmetry. The spontaneous PT\cal{PT}PT-symmetry breaking emerges when the strength of the imaginary part of the kicking potential exceeds a threshold value. We find, both analytically and numerically, that in the broken phase of PT\cal{PT}PT symmetry, the OTOCs rapidly saturate with time evolution. Interestingly, the late-time saturation value scales as a pow-law in the system size. The mechanism of such scaling law results from the interplay between the effects of nonlocal operator in OTOCs and the time reversal induced by non-Hermitian driven potential.
Ballistic diffusion vs. damped oscillation of energy in a PT\mathcal{PT}PT-symmetric quantum kicked harmonic oscillator
We numerically study the quantum dynamics of a PT\mathcal{PT}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.
We investigate the dynamics of the out-of-time-order correlators (OTOCs) via a non-Hermitian extension of the quantum kicked rotor model, where the kicking potential satisfies PT -symmetry. The spontaneous PT -symmetry breaking emerges when the strength of the imaginary part of the kicking potential exceeds a threshold value. We find, both analytically and numerically, that in the broken phase of PT symmetry, the OTOCs rapidly saturate with time evolution. Interestingly, the late-time saturation value scales as a pow-law in the system size. The mechanism of such scaling law results from the interplay between the effects of the nonlocal operator in OTOCs and the time reversal induced by non-Hermitian-driven potential.
We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with P T symmetry. For the quantum dynamics, both the mean momentum and mean square of momentum exhibit the staircase growth with time when the system parameter is in the neighborhood of the P T symmetry breaking point. If the system parameter is much larger than the P T symmetry breaking point, the accelerator mode results in the directed spreading of the wavepackets as well as the ballistic diffusion in momentum space. For the classical dynamics, the non-Hermitian kicking potential leads to the exponentially-fast increase of classical complex trajectories. As a consequence, the imaginary part of the trajectories exponentially diffuses with time, while the real part exhibits the normal diffusion. Our analytical prediction of the exponential diffusion of imaginary momentum and its breakdown time is in good agreement with numerical results. The quantum signature of the chaotic diffusion of the complex trajectories is reflected by the dynamics of the out-of-time-order correlators (OTOC). In the semiclassical regime, the rate of the exponential increase of the OTOC is equal to that of the exponential diffusion of the complex trajectories.