Dynamical thermalization, Rayleigh–Jeans condensate, vortexes and wave collapse in quantum chaos fibers and fluid of light

Abstract

We study analytically and numerically the time evolution of a nonlinear field described by the nonlinear Schrödinger equation in a chaotic D-shape billiard. In the absence of nonlinearity the systemhas standard properties of quantum chaos. This model describes a longitudinal light propagationin a multimode D-shape optical fiber and also those in a Kerr nonlinear medium of atomic vapor.We show that, above a certain chaos border of nonlinearity, chaos leads to dynamical thermalization with the Rayleigh–Jeans (RJ) thermal distribution and the formation of the RJ condensate ina vicinity of the ground state accumulating about 80%–90% of total probability. Certain similarities of this phenomenon with the Fröhlich condensate are discussed. Below the chaos border thedynamics is quasi-integrable corresponding to the Kolmogorov–Arnold–Moser integrability. Wealso describe the time evolution during the process of relaxation to the thermal state and the timedependence of quantum von Neumann and classical Boltzmann entropies during this process. Ata strong focusing nonlinearity we show that the wave collapse can take place even at sufficientlyhigh positive energy being very different from the open space case. Finally for the defocusing casewe establish the superfluid regime for vortex dynamics at strong nonlinearity. System parametersfor optical fiber experimental studies of these effects are also discussed.