Diffusion of Power in Randomly Perturbed Hamiltonian Partial Differential Equations

@inproceedings{Kirr2004DiffusionOP,
title={Diffusion of Power in Randomly Perturbed Hamiltonian Partial Differential Equations},
author={E. W. Kirr and Michael I. Weinstein},
year={2004}
}

We study the evolution of the energy (mode-power) distribution for a class of randomly perturbed Hamiltonian partial differential equations and derive master equations for the dynamics of the expected power in the discrete modes. In the case where the unperturbed dynamics has only discrete frequencies (finitely or infinitely many) the mode-power distribution is governed by an equation of discrete diffusion type for times of order O(ε−2). Here ε denotes the size of the random perturbation. If… CONTINUE READING