Hopping with time-dependent disorder

TL;DR

This paper investigates the propagation of a quantum particle in a disordered lattice with time-dependent hopping disorder, revealing diffusive behavior and complex excitonic dynamics influenced by an external bias.

Contribution

It introduces a model combining time-dependent hopping disorder with bias, deriving an effective Liouvillian and analyzing excitonic motion in this context.

Findings

The system exhibits diffusive behavior despite disorder.

Bias leads to excitonic states with unique dispersion laws.

Transition probabilities are governed by competition between single and pair hopping.

Abstract

We determine the propagation properties of a quantum particle in a d-dimensional lattice with hopping disorder, delta-correlated in time. The system is delocalized: the averaged transition probability shows a diffusive behavior. Then, superimposed to the disorder, we consider a bias favouring the motion with a given orientation, as in the dynamics of flux lines in superconductors. The result is an effective Liouvillian for the density matrix, which is characterized by competition between single particle and pair hopping. In this case the transition probability is determined in terms of excitonic motion, each exciton being extended along the bias direction and characterized by a nontrivial dispersion law.