Non-equilibrium dynamics of nonlinear wave systems: Turbulent regime, breakdown and wave condensation

Abstract

This thesis concerns two different subjects. Although, these two kind of problems are related to the statistical description of systems with many degrees of freedom, they are of quite different nature. The first part of this work deals with the study of weakly non linear wave systems. The well-established wave turbulence theory is applied to different systems, studying the validity and limitations of it. More precisely, the long-time statistical properties for elastic waves in plates and shells, and capillary waves in fluids are considered in terms of a kinetic equation for the distribution of spectral densities. Turbulent regime, dissipation effect and the non-dispersive limit are analyzed among other situations. Finally, the description of the dynamic of wave condensate is introduced, extending the wave turbulence theory to include this simple coherent structure. In the second part we have studied the sign problem, which represents a major limitation in many numerical simulations. A good comprehension of the statistical mechanics of Monte Carlo sampling with the sign problem is achieved by analogy with glassy systems. A novelty approach by means of quantum annealing is also proposed, which far from solve the sign problem gives a deeper insight into the structure of it.