Simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities.

Abstract

The localization of energy in the discrete nonlinear Schrödinger equation is explained with statistical methods. The partition function and the entropy of the system are computed for low-amplitude initial conditions. Detailed predictions for the long-time solution are derived. Localized high-amplitude excitations absorb a surplus of energy when they emerge as a by-product of the production of entropy in the small fluctuations. The thermodynamic interpretation of this process applies to many dynamical systems with two conserved quantities.