# Coupled transport in a linear-stochastic Schr\"odinger Equation

## TL;DR

This paper investigates heat and norm transport in a one-dimensional lattice of linear Schrödinger oscillators with stochastic perturbations, revealing diffusive behavior and finite transport coefficients under nonequilibrium conditions.

## Contribution

It introduces a model of coupled heat and norm transport in a stochastic Schrödinger lattice and characterizes its diffusive transport properties and nonequilibrium behavior.

## Key findings

- Diffusive transport observed in the lattice.
- Finite Onsager and Seebeck coefficients in the thermodynamic limit.
- Equilibrium properties match those of the Discrete Nonlinear Schrödinger equation at low nonlinearity.

## Abstract

I study heat and norm transport in a one-dimensional lattice of linear Schr\"odinger oscillators with conservative stochastic perturbations. Its equilibrium properties are the same of the Discrete Nonlinear Schr\"odinger equation in the limit of vanishing nonlinearity. When attached to external classical reservoirs that impose nonequilibrium conditions, the chain displays diffusive transport, with finite Onsager coefficients in the thermodynamic limit and a finite Seebeck coefficient.