Diffusion of Power in Randomly Perturbed Hamiltonian Partial Differential Equations
| dc.creator | Kirr, E. | |
| dc.creator | Weinstein, M. I. | |
| dc.date | 2003-11-11 | |
| dc.date.accessioned | 2026-07-07T05:35:05Z | |
| dc.date.available | 2026-07-07T05:35:05Z | |
| dc.description | We study the evolution of the energy (mode-power) distribution for a class of randomly perturbed Hamiltonian partial differential equations and derive {\it 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 $\cO(\ve^{-2})$. Here $\ve$ denotes the size of the random perturbation. If the unperturbed system has discrete and continuous spectrum the mode-power distribution is governed by an equation of discrete diffusion-damping type for times of order $\cO(\ve^{-2})$. The methods involve an extension of the authors' work on deterministic periodic and almost periodic perturbations, and yield new results which complement results of others, derived by probabilistic methods. | |
| dc.description | 51 pages LaTex | |
| dc.identifier | https://arxiv.org/abs/nlin/0311020 | |
| dc.identifier | http://arxiv.org/abs/nlin/0311020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80599 | |
| dc.subject | Adaptation and Self-Organizing Systems | |
| dc.title | Diffusion of Power in Randomly Perturbed Hamiltonian Partial Differential Equations | |
| dc.type | text |