Nonlinear defect theory of thermal relaxation in complex multimoded systems

Abstract

We show that a single nonlinear defect can thermalize an initial excitation towards a Rayleigh-Jeans (RJ) state in complex multimoded systems. The thermalization can be hindered by disorder-induced localization phenomena, which drive the system into a metastable RJ state. It can differ dramatically from the thermal RJ and it involves only a (quasi)isolated set of prethermal modes whose density can be predicted using a renormalization group theory. Importantly, we establish a connection between the modal relaxation rates that dictate the dynamics towards (quasi)equilibrium and the Thouless conductance. This connection allows us to derive the whole modal relaxation rate distribution. Our results are relevant to photonics, optomechanics, and cold atoms.