We explore the statistical behaviour of the discrete nonlinear Schrödinger equation as a test bed for the observation of negative-temperature (i.e. above infinite temperature) states in Bose–Einstein condensates in optical lattices and arrays of optical waveguides. By monitoring the microcanonical temperature, we show that there exists a parameter region where the system evolves towards a state characterized by a finite density of discrete breathers and a negative temperature. Such a state persists over very long (astronomical) times since the convergence to equilibrium becomes increasingly slower as a consequence of a coarsening process. We also discuss two possible mechanisms for the generation of negative-temperature states in experimental setups, namely, the introduction of boundary dissipations and the free expansion of wavepackets initially in equilibrium at a positive temperature.
- discrete breathers
- optical waveguides
- negative temperatures
Iubini, S., Franzosi, R., Livi, R., Oppo, G-L., & Politi, A. (2013). Discrete breathers and negative-temperature states. New Journal of Physics, 15(2), . https://doi.org/10.1088/1367-2630/15/2/023032