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 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).
Kalmykov
Yuri P
YP
Lab. Mathématiques et Physique des Systèmes, Université de Perpignan, 52 Avenue de Paul Alduy, 66860 Perpignan Cedex, France.
Coffey
William T
WT
Titov
Sergey V
SV