TY - JOUR

T1 - Diffusion of power in randomly perturbed Hamiltonian partial differential equations

AU - Kirr, E.

AU - Weinstein, M. I.

N1 - Copyright:
Copyright 2005 Elsevier B.V., All rights reserved.

PY - 2005/4

Y1 - 2005/4

N2 - 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 script O sign(ε-2). Here ε 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 script O sign(ε-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.

AB - 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 script O sign(ε-2). Here ε 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 script O sign(ε-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.

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U2 - 10.1007/s00220-004-1273-6

DO - 10.1007/s00220-004-1273-6

M3 - Article

AN - SCOPUS:15244353409

SN - 0010-3616

VL - 255

SP - 293

EP - 328

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -