Negative Temperature States in the Discrete Nonlinear Schroedinger   Equation
  We explore the statistical behavior of the discrete nonlinear Schroedinger equation. We find a parameter region where the system evolves towards a state characterized by a finite density of breathers and a negative temperature. Such a state is metastable but the convergence to equilibrium occurs on astronomical time scales and becomes increasingly slower as a result of a coarsening processes. Stationary negative-temperature states can be experimentally generated via boundary dissipation or from free expansions of wave packets initially at positive temperature equilibrium. 
S. Iubini, R. Franzosi, R. Livi, G.-L. Oppo, A. Politi
nlin.PS cond-mat.quant-gas