Crossover between ballistic and diffusive transport: The Quantum Exclusion Process

TL;DR

This paper investigates how free fermions in one dimension transition from ballistic to diffusive transport due to combined coherent and stochastic effects, providing analytical solutions and identifying the crossover timescale.

Contribution

It introduces a class of noise terms leading to decoupled correlation equations and explicitly solves for two-point functions in a specific hopping model.

Findings

Analytical Green's function for particle density derived.

Identified timescale for crossover from ballistic to diffusive transport.

Demonstrated competition between coherent and stochastic conduction channels.

Abstract

We study the evolution of a system of free fermions in one dimension under the simultaneous effects of coherent tunneling and stochastic Markovian noise. We identify a class of noise terms where a hierarchy of decoupled equations for the correlation functions emerges. In the special case of incoherent, nearest-neighbour hopping the equation for the two-point functions is solved explicitly. The Green's function for the particle density is obtained analytically and a timescale is identified where a crossover from ballistic to diffusive behaviour takes place. The result can be interpreted as a competition between the two types of conduction channels where diffusion dominates on large timescales.