Quantum diffusion: a simple, exactly solvable model

TL;DR

This paper introduces an exactly solvable quantum model that describes the time evolution of diffusion currents between two fermion reservoirs, revealing power-law decay and entropy production characteristics.

Contribution

It presents a simple, analytical quantum model for diffusion between fermion reservoirs, providing exact solutions for transient and steady-state behaviors.

Findings

Transient diffusion current exhibits power-law decay.

Entropy production is proportional to the diffusion current.

Steady state characterized by different densities or chemical potentials.

Abstract

We propose a simple quantum mechanical model describing the time dependent diffusion current between two fermion reservoirs that were initially disconnected and characterized by different densities or chemical potentials. The exact, analytical solution of the model yields the transient behavior of the coupled fermion systems evolving to a final steady state, whereas the long-time behavior is determined by a power law rather than by exponential decay. Similar results are obtained for the entropy production which is proportional to the diffusion current.