Work

Superexponential diffusion in nonlinear non-Hermitian systems

Year: 2020

Type: article

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.

Source: Physical Review A

DOI: 10.1103/physreva.102.062213

Authors: Wen-Lei Zhao, Longwen Zhou, Jie Liu, Peiqing Tong, Kaiqian Huang