Off-equilibrium Langevin dynamics of the discrete nonlinear Schroedinger chain

Suitable Langevin thermostats are introduced which are able to control both the temperature and the chemical potential of a one-dimensional lattice of nonlinear Schr\"odinger oscillators. The resulting non-equilibrium stationary states are then investigated in two limit cases (low temperatures and large particle densities), where the dynamics can be mapped onto that of a coupled-rotor chain with an external torque. As a result, an effective kinetic definition of temperature can be introduced and compared with the general microcanonical (global) definition.