  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.
