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We study numerically how the energy spreads over a finite disorderednonlinear one-dimensional lattice, where all linear modes are exponentiallylocalized by disorder. We establish emergence of dynamical thermalization,characterized as an ergodic chaotic dynamical state with a Gibbs distributionover the modes. Our results show that the fraction of thermalizing modes isfinite and grows with the nonlinearity strength.

Dynamical Thermalization of Disordered Nonlinear Lattices