Talk at I Conference of the Italian Society of Statistical Physics - SIFS
Date:
Title: Discrete Non-Linear Schrodinger Equation: Localization and Geometry (Video)
Abstract: The Discrete Non-Linear Schrodinger (DNLS) model is well known to display a high energy-density phase in which the equivalence between statistical ensambles is not valid. In this phase, the charge accumulates on few sites and resides there for times that diverge quickly in the thermodynamic limit. As a consequence, in such regime the dynamics of the system shows breaking of ergodicity. In this talk I will argue that such localization mechanism can be attributed, in a mean-field scenario, to some geometric properties of the microcanonical potential energy surface, that we characterize using Morse theory. Moreover, I will also show that this localization transition coincides with a phase transition in the lowest eigenvalue of the Laplacian on said surface, once the Hamiltonian motion is substituted with a Brownian motion.