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 system has standard properties of quantum chaos. This model describes a longitudinal light propagation in 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 in a 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 the dynamics is quasi-integrable corresponding to the Kolmogorov–Arnold–Moser integrability. We also describe the time evolution during the process of relaxation to the thermal state and the time dependence of quantum von Neumann and classical Boltzmann entropies during this process. At a strong focusing nonlinearity we show that the wave collapse can take place even at sufficiently high positive energy being very different from the open space case. Finally for the defocusing case we establish the superfluid regime for vortex dynamics at strong nonlinearity. System parameters for optical fiber experimental studies of these effects are also discussed.