Fourier's law on a one-dimensional optical random lattice

TL;DR

This paper investigates how random fluctuations in a one-dimensional optical lattice affect transport properties, demonstrating that the steady-state current follows Fourier's law with a linear density profile.

Contribution

It analytically shows that lattice fluctuations lead to a linear density profile and Fourier's law behavior in a one-dimensional bosonic lattice system.

Findings

Steady-state density is linear across the system.

Local current obeys Fourier's law with a fluctuation-dependent conductivity.

Lattice fluctuations influence transport properties in the system.

Abstract

We study the transport properties of a one-dimensional hard-core bosonic lattice gas coupled to two particle reservoirs at different chemical potentials which generate a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary-state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law $j=-\kappa(\tau)\nabla n $ where $\tau$ is a typical timescale of the lattice fluctuations and $\nabla n$ the density gradient imposed by the reservoirs.