Transition behavior of the discrete nonlinear Schrödinger equation.

Many nonlinear lattice systems exhibit high-amplitude localized structures, or discrete breathers. Such structures emerge in the discrete nonlinear Schrödinger equation when the energy is above a critical threshold. This paper studies the statistical mechanics at the transition and constructs the probability distribution in the regime where breathers emerge. The entropy as a function of the energy is nonanalytic at the transition. The entropy is independent of the energy in the regime of breathers above the transition.