Incoherent ensemble dynamics in disordered systems

TL;DR

This paper derives a quantum master equation to describe how ensemble-averaged states in disordered systems transition from quantum coherence to classical mixtures, linking disorder correlations to decoherence.

Contribution

It introduces a novel master equation framework that captures short-time ensemble-averaged dynamics in disordered quantum systems, connecting disorder effects to collisional decoherence.

Findings

The master equation reflects translational invariance of disorder correlations.

Disorder correlations influence the spatial decay of coherences.

Application to the 1D Anderson model demonstrates the theory's relevance.

Abstract

We derive a quantum master equation which describes the dynamics of the ensemble-averaged state of homogeneous disorder models at short times, and mediates a transition from coherent superpositions into classical mixtures. While each single realization follows unitary dynamics, this decoherencelike behavior arises as a consequence of the ensemble average. The master equation manifestly reflects the translational invariance of the disorder correlations and allows us to relate the disorder-induced dynamics to a collisional decoherence process, where the disorder correlations determine the spatial decay of coherences. We apply our theory to the (one-dimensional) Anderson model.