Out-of-equilibrium bosons on a one-dimensional optical random lattice

TL;DR

This paper investigates how random lattice fluctuations affect the steady-state transport properties of a one-dimensional hard-core boson system connected to reservoirs, revealing a linear density profile and Fourier law behavior.

Contribution

It analytically demonstrates the impact of lattice randomness on steady-state density and current in a 1D bosonic system, linking fluctuation timescale to transport laws.

Findings

Steady-state density profile is linear.

Local current obeys Fourier law with fluctuation-dependent conductivity.

Lattice randomness influences transport properties.

Abstract

We study the transport properties of a one-dimensional hard-core boson lattice gas coupled to two particle reservoirs at different chemical potentials generating 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 \rho $ where $\tau$ is a typical timescale of the lattice fluctuations and $\nabla \rho$ the density gradient imposed %on the system by the reservoirs.