Inertial Effects in the Fractional Translational Brownian Motion in a Double-Well Potential - COFFEY, WILLIAM THOMAS; KALYMYKOV, YURI PETROVICH (My University, 2007)
The anomalous translational diffusion including inertial effects of nonlinear Brownian oscillators in a double well potential V(x)=ax2?2+bx4?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).
PUBLISHED
Keywords: Brownian oscillators; Physics