title: Inertial effects in the fractional translational diffusion of a Brownian particle in a double-well potential.
abstract: 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).
authors.affiliation: Lab. Mathématiques et Physique des Systèmes, Université de Perpignan, 52 Avenue de Paul Alduy, 66860 Perpignan Cedex, France.
authors.forename: Yuri P
authors.initials: YP
authors.lastname: Kalmykov
authors.forename: William T
authors.initials: WT
authors.lastname: Coffey
authors.forename: Sergey V
authors.initials: SV
authors.lastname: Titov