The nonequilibrium discrete nonlinear Schroedinger equation

TL;DR

This paper investigates the nonequilibrium steady states of the one-dimensional discrete nonlinear Schroedinger equation, revealing normal transport behavior, variable Seebeck coefficients, and complex density and temperature profiles influenced by system parameters.

Contribution

It introduces a detailed study of coupled transport in the DNLS model with Monte Carlo thermostats, highlighting the finiteness of Onsager coefficients and the conditions for normal transport.

Findings

Transport is normal with finite Onsager coefficients.

Seebeck coefficient can be positive or negative depending on parameters.

Density and temperature profiles can become nonmonotonic under large thermostat differences.

Abstract

We study nonequilibrium steady states of the one-dimensional discrete nonlinear Schroedinger equation. This system can be regarded as a minimal model for stationary transport of bosonic particles like photons in layered media or cold atoms in deep optical traps. Due to the presence of two conserved quantities, energy and norm (or number of particles), the model displays coupled transport in the sense of linear irreversible thermodynamics. Monte Carlo thermostats are implemented to impose a given temperature and chemical potential at the chain ends. As a result, we find that the Onsager coefficients are finite in the thermodynamic limit, i.e. transport is normal. Depending on the position in the parameter space, the "Seebeck coefficient" may be either positive or negative. For large differences between the thermostat parameters, density and temperature profiles may display an unusual nonmonotonic shape. This is due to the strong dependence of the Onsager coefficients on the state variables.