Super-exponential diffusion in nonlinear non-Hermitian systems
- URL: http://arxiv.org/abs/2010.01975v1
- Date: Mon, 5 Oct 2020 13:04:23 GMT
- Title: Super-exponential diffusion in nonlinear non-Hermitian systems
- Authors: Wen-Lei Zhao, Longwen Zhou, Jie Liu, Peiqing Tong, Kaiqian Huang
- Abstract summary: We investigate the quantum diffusion of a periodically kicked particle subjecting to both nonlinearity induced self-interactions and $mathcalPT$-symmetric potentials.
In the $mathcalPT$-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 super-exponential growth of the mean energy.
- Score: 2.8572548342403024
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We investigate the quantum diffusion of a periodically kicked particle
subjecting 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 mean square of
momentum scales with time in a super-exponential form $\langle
p^2(t)\rangle\propto\exp[\beta\exp(\alpha t)]$, 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 super-exponential growth of the mean energy.
These theoretical predictions are in good agreement with numerical simulations
in a $\cal{PT}$-symmetric nonlinear kicked particle. Our discovery establishes
a new mechanism of diffusion in interacting and dissipative quantum systems.
Important implications and possible experimental observations are discussed.
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