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

The anomalous translational diffusion including inertial effects of nonlinear Brownian oscillators in a double well potential V(x)=ax{2}/2+bx{4}/4 is considered. An exact solution of the fractional Klein-Kramers (Fokker-Planck) equation is obtained allowing one to calculate via matrix continued frac...

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Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2007-03, Vol.75 (3 Pt 1), p.031101-031101, Article 031101
Main Authors: Kalmykov, Yuri P, Coffey, William T, Titov, Sergey V
Format: Article
Language:English
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Summary:The anomalous translational diffusion including inertial effects of nonlinear Brownian oscillators in a double well potential V(x)=ax{2}/2+bx{4}/4 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).
ISSN:1539-3755
1550-2376
DOI:10.1103/physreve.75.031101