https://doi.org/10.1007/s100510050832
Fokker-Planck dynamics in a bistable periodic potential
Laboratoire de Physique de la Matière Condensée, Faculté des Sciences Ben M'sik,
Casablanca, BP 7955, Morocco
Corresponding author: a cui@techno.net.ma
Received:
25
May
1998
Revised:
15
November
1998
Published online: 15 July 1999
Dynamic properties of Brownian particles immersed in a periodic potential
with two barriers V1 and V2 (symmetric bistable potential) are
studied by using the Fokker-Planck equation which we solve numerically by
the matrix continued fraction method. This study will therefore serve to
demonstrate the influence of this form of potential, which is of great
interest for superionic conductors and for many other solid systems, on the
diffusion process. Thus, we have calculated the full width at half maximum
(FWHM) λ(q) of the quasi-elastic line of the dynamic structure
factor, for a large range of values of the wave-vectors q. Our results show
clearly that, by varying the ratio of the barriers
strictly between 0 and 1, the Fokker-Planck equation describes a
diffusive process which has some characteristic of jump and liquid-like
regimes. While in the limit cases, i.e. when
tends to 0 or 1,
the diffusion process can be described only by a simple jump motion.
However, the jump-lengths corresponding to each limit case are not equal. In
general the change of the ratio is found to have a significant effect on the
character of the diffusive motion. We have also performed Fokker-Planck
dynamics calculations of the diffusion coefficient in a bistable potential. We
have found a good agreement between numerical calculations and analytical
approximation results obtained in the high friction limit.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 82.20.Fd – Stochastic and trajectory models, other theories and models / 05.60.-k – Transport processes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999