Weak chaos and Arnold diffusion in the strongly disordered nonlinear Schroedinger chain
Denis Basko, LPMMC – Université Joseph Fourier
I will discuss the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators, which is one of the simplest models allowing to study the effect of a classical nonlinearity on the Anderson localization. The system has chaotic behavior, and it is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of relaxation at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids.