Inertial effects in the fractional translational diffusion of a Brownian particle in a double-well potential

Yuri P. Kalmykov, William T. Coffey, and Sergey V. Titov
Phys. Rev. E 75, 031101 – Published 1 March 2007

Abstract

The anomalous translational diffusion including inertial effects of nonlinear Brownian oscillators in a double well potential V(x)=ax22+bx44 is considered. An exact solution of the fractional Klein-Kramers (Fokker-Planck) equation is obtained allowing one to calculate via matrix continued fractions the positional autocorrelation function and dynamic susceptibility describing the position response to a small external field. The result is a generalization of the solution for the normal Brownian motion in a double well potential to fractional dynamics (giving rise to anomalous diffusion).

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  • Received 31 October 2006

DOI:https://doi.org/10.1103/PhysRevE.75.031101

©2007 American Physical Society

Authors & Affiliations

Yuri P. Kalmykov

  • Lab. Mathématiques et Physique des Systèmes, Université de Perpignan, 52, Avenue de Paul Alduy, 66860 Perpignan Cedex, France

William T. Coffey

  • Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland

Sergey V. Titov

  • Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Vvedenskii Square 1, Fryazino, Moscow Region, 141190, Russian Federation

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Issue

Vol. 75, Iss. 3 — March 2007

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