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arXiv:2010.01975 · Physical Review A

Superexponential diffusion in nonlinear non-Hermitian systems

Wen-Lei Zhao, Longwen Zhou, Jie Liu, Peiqing Tong, Kai-Qian Huang

Published Dec 18, 2020• 17 citations
arXivHTMLPDF

Abstract

We investigate the quantum diffusion of a periodically kicked particle subjected to both nonlinearity-induced self-interactions and $\mathcal{PT}$-symmetric potentials. We find that, due to the interplay between the nonlinearity and non-Hermiticity, the expectation value of the mean square of momentum scales with time in a superexponential form $\ensuremath{\langle}{p}^{2}(t)\ensuremath{\rangle}\ensuremath{\propto}exp[\ensuremath{\beta}exp(\ensuremath{\alpha}t)]$, which is faster than any known rates of quantum diffusion. In the $\mathcal{PT}$-symmetry-breaking phase, the intensity of a state increases exponentially with time, leading to the exponential growth of the interaction strength. The feedback of the intensity-dependent nonlinearity further turns the interaction energy into the kinetic energy, resulting in a superexponential growth of the mean energy. These theoretical predictions are in good agreement with numerical simulations in a $\mathcal{PT}$-symmetric nonlinear kicked particle. Our discovery establishes a mechanism of diffusion in interacting and dissipative quantum systems. Important implications and possible experimental observations are discussed.

DOI
10.1103/physreva.102.062213

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We numerically investigate the quantum transport in coupled kicked rotors with PT\mathcal{PT}PT-symmetric potential. We find that spontaneous PT\mathcal{PT}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 PT\mathcal{PT}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.
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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