Diffusion and superdiffusion of energy in one dimensional systems of oscillators

Non-equilibrium Dynamics and Random Matrices
Topic:Diffusion and superdiffusion of energy in one dimensional systems of oscillators
Speaker:Stefano Olla
Affiliation:Dauphine Universite Paris
Date:Thursday, November 21
Time/Room:3:00pm - 4:00pm/Dilworth Room
Video Link:https://video.ias.edu/nedrm/2013/1121-StefanoOlla

We consider a system of harmonic oscillators with stochastic perturbations of the dynamics that conserve energy and momentum. In the one dimensional unpinned case, under proper space-time rescaling, Wigner distribution of energy converges to the solution of a fractional heat equation (with power 3/4 for the laplacian). For pinned systems or in dimension 3 or higher, we prove normal diffusive behaviour. Similar results are also obtained for space-time energy correlations in equilibrium. This is in agreement with previous 'weak noise' limits, passing through a kinetic equation, and conjectured behaviour for beta-FPU chains (quartic symmetric interaction). Joint works with Tomasz Komorowski and Giada Basile.