# Emergence of Classical Random Walk from Non-Hermitian Effects in Quantum Kicked Rotor

## TL;DR

This paper shows how non-Hermitian effects in a quantum system can lead to classical random walk behavior in momentum space.

## Contribution

The study reveals how non-Hermitian potentials induce classical random walks and affect quantum entanglement in kicked rotor systems.

## Key findings

- Momentum variance transitions from quadratic to linear growth under non-Hermitian conditions.
- Non-Hermitian effects produce Gaussian momentum distributions resembling classical random walks.
- Non-Hermiticity enhances quantum entanglement while deviations from resonance reduce it.

## Abstract

We investigate the quantum random walk in momentum space of a spinor kicked rotor with a non-Hermitian kicking potential. We find that the variance in momentum distributions transitions from quadratic to linear growth over time for the non-Hermitian case. Correspondingly, the momentum distributions are in the shape of Gaussian wavepackets, providing clear evidence of a classical random walk induced by the non-Hermitian-driven potential. Remarkably, the rate of the linear growth of the variance diverges as the non-Hermitian parameter approaches zero. In the Hermitian case, deviations from the quantum resonance condition dramatically suppress the quadratic growth of the variance, leading to dynamical localization of the quantum walk. Under such quantum non-resonance conditions, the classical random walk is significantly reduced by the non-Hermitian-driven potential. Interestingly, non-Hermiticity enhances quantum entanglement between internal degrees of freedom, while deviations from the quantum resonance condition reduce it. Possible applications of our findings are discussed.