  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.
