Interplay of thermalization and strong disorder: Wave turbulence theory, numerical simulations, and experiments in multimode optical fibers

Abstract

We address the problem of thermalization in the presence of a time-dependent disorder in the framework of the nonlinear Schrödinger (or Gross-Pitaevskii) equation with a random potential. The thermalization to the Rayleigh-Jeans distribution is driven by the nonlinearity. On the other hand, the structural disorder is responsible for a relaxation toward the homogeneous equilibrium distribution (particle equipartition), which thus inhibits thermalization (energy equipartition). On the basis of the wave turbulence theory, we derive a kinetic equation that accounts for the presence of strong disorder. The theory unveils the interplay of disorder and nonlinearity. It unexpectedly reveals that a non-equilibrium process of condensation and thermalization can take place in the regime where disorder effects dominate over nonlinear effects. We validate the theory by numerical simulations of the nonlinear Schrödinger equation and the derived kinetic equation, which are found in quantitative agreement without using adjustable parameters. Experiments realized in multimode optical fibers with an applied external stress evidence the process of thermalization in the presence of strong disorder.

12 pages, 7 figures

References in corpus (8)

• Transmission of natural scene images through a multimode fibre
• Thermodynamic theory of highly multimoded nonlinear optical systems
• Nonlinear propagation in multi-mode fibers in the strong coupling regime
• Soliton trapping in multimode fibers with random mode coupling
• Dramatic acceleration of wave condensation mediated by disorder in multimode fibers
• Dissipative dynamics of superfluid vortices at non-zero temperatures
• Thermalization of light's orbital angular momentum in nonlinear multimode waveguide systems
• Wave condensation with weak disorder versus beam self-cleaning in multimode fibers

Cited by in corpus (8)

• Observation of light thermalization to negative temperature Rayleigh-Jeans equilibrium states in multimode optical fibers
• Rayleigh-Jeans thermalization vs beam cleaning in multimode optical fibers
• Random matrix model of Kolmogorov-Zakharov turbulence
• A general multi-wave quasi-resonance theory for lattice energy diffusion
• Spatio-temporal thermalization and adiabatic cooling of guided light waves
• Irreversible thermalization vs reversible dynamics mediated by anomalous correlators: Wave turbulence theory and experiments in optical fibers
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport
• Spatio-temporal equilibrium thermodynamics of guided optical waves at positive and negative temperatures