Quantum walk in stochastic environment

TL;DR

This paper introduces a quantum version of the Sinai-Derrida model using Lindblad dynamics, revealing a delocalization transition and enhanced disorder effects due to quantum coherence in a stochastic environment.

Contribution

It presents a novel quantum model for random walks in random environments and analyzes the effects of quantum coherence on localization and disorder enhancement.

Findings

Delocalization transition occurs at a critical bias.

Quantum coherence enhances effective disorder.

Spectrum behavior depends non-monotonically on transition rates.

Abstract

We consider a quantized version of the Sinai-Derrida model for "random walk in random environment". The model is defined in terms of a Lindblad master equation. For a ring geometry (a chain with periodic boundary condition) it features a delocalization-transition as the bias in increased beyond a critical value, indicating that the relaxation becomes under-damped. Counter intuitively, the effective disorder is enhanced due to coherent hopping. We analyze in detail this enhancement and its dependence on the model parameters. The non-monotonic dependence of the Lindbladian spectrum on the rate of the coherent transitions is highlighted.