Abstract
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.
Highlights
Negative Temperature States in the Discrete Nonlinear Schrodinger EquationWe find a parameter region where the system evolves towards a state characterized by a finite density of breathers and a negative temperature
We explore the statistical behavior of the discrete nonlinear Schrodinger equation
With the help of an explicit expression for the microcanonical temperature [9], we are able to show that a broad class of initial conditions (IC) of the discrete nonlinear Schrodinger (DNLS) equation converges towards a well defined thermodynamic state characterized by a negative temperature and a finite density of breathers
Summary
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. The discrete nonlinear Schrodinger (DNLS) equation has been widely investigated as a semiclassical model for Bose-Einstein condensates (BEC) in optical lattices and for light propagation in arrays of optical waveguides [1]. With the help of an explicit expression for the microcanonical temperature [9], we are able to show that a broad class of initial conditions (IC) of the DNLS equation converges towards a well defined thermodynamic state characterized by a negative temperature and a finite density of breathers. The sign of the first term in the r.h.s. is assumed to be positive, since h 0.4 h
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