Statistical Mechanics of DNLS

In this section, we focus our attention on the long-time asymptotics of the system, aiming to understand the dynamics from the viewpoint of statistical mechanics. The study of the thermalization of the lattice for T ≥ 0 was performed analytically as well as numerically in [1]. In that work, a regime in phase space was identified wherein regular statistical mechanics considerations apply, and hence, thermalization was observed numerically and explored analytically using regular, grand-canonical, Gibbsian equilibrium measures. However, the nonlinear dynamics of the problem renders permissible the realization of regimes of phase space which would formally correspond to “negative temperatures” in the sense of statistical mechanics. The novel feature of these states was found to be that the energy spontaneously localizes in certain lattice sites forming breather-like excitations.