Gaussian Convergence for Stochastic Acceleration of Particles in the Dense Spectrum Limit

The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant modulo π /2 and the power spectrum expectation is uniform....

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Bibliographic Details
Published inJournal of statistical physics Vol. 148; no. 3; pp. 591 - 605
Main Author Elskens, Yves
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.08.2012
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Propagation of chaos
Fokker–Planck equation
Wave–particle interaction
Weak plasma turbulence
Stochastic acceleration
Hamiltonian chaos
Quasilinear diffusion
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Summary:The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant modulo π /2 and the power spectrum expectation is uniform. The proof provides a full probabilistic foundation to the quasilinear approximation in this limit. The result extends to an arbitrary number of particles, founding the use of the ensemble picture for their behaviour in a single realization of the stochastic wave field.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-012-0546-2