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

TL;DR

This paper investigates how nonlinear chaotic optical systems evolve towards thermal equilibrium, forming condensates and vortex structures, with implications for optical fibers and fluid light experiments.

Contribution

It analytically and numerically demonstrates dynamical thermalization, Rayleigh-Jeans condensate formation, and vortex dynamics in nonlinear chaotic optical systems, linking quantum chaos and wave collapse phenomena.

Findings

Chaos induces thermalization with Rayleigh-Jeans distribution

Condensate accumulates 80-90% of probability near ground state

Wave collapse occurs at high positive energy in focusing nonlinearity

Abstract

We study analytically and numerically the time evolution of a nonlinear field described by the nonlinear Schr\"odinger equation in a chaotic $D$-shape billiard. In 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 thermal distribution and the formation of the Rayleigh-Jeans condensate in a vicinity of the ground state accumulating in it about 80-90\% of total probability. Certain similarities of this phenomenon with the Fr\"ohlich condensate are discussed. Below the chaos border the dynamics is quasi-integrable corresponding to the Kolmogorov-Arnold-Moser integrability. We describe also 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.