Off-equilibrium Langevin dynamics of the discrete nonlinear Schrödinger chain

We introduce suitable Langevin thermostats which are able to control both the temperature and the chemical potential of a one-dimensional lattice of nonlinear Schrödinger oscillators. The resulting nonequilibrium stationary states are then investigated in the limit of 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.