𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Diffusion of a particle under a square-well potential

✍ Scribed by Akio Morita

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
347 KB
Volume
69
Category
Article
ISSN
0167-7322

No coin nor oath required. For personal study only.

✦ Synopsis

The dynamics of Brownian motion of a particle whose position is represented by x under a square-well potential which has infinite and finite barriers at x = 0 and x = u, respectively, and elsewhere is flat has been investigated and exact results are obtained. Particularly when the potential depth in 0 2 .x < u is relatively large, it is found that there exists a time region where the dynamics becomes very slow and the mean-square displacement deviates highly from the usual Einstein's relation. This is due to the fact that it needs rather long time for the particle to escape from the barrier repeating many insufficiently strong collisions with the wall at x = u, which is similar to the reaction dynamics. The probability density and the number of particles within 0 I x < u are also worked out exactly.

πŸ“œ SIMILAR VOLUMES

Escape by diffusion from a square well a
Escape by diffusion from a square well across a square barrier
✍ B.U. Felderhof πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 259 KB

The problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one-dimensional Smoluchowski equation for the space-and time-dependent probability distribution. For the model potential the Smoluchowski equation is solved exactly by

Self-diffusion coefficients of dense flu
Self-diffusion coefficients of dense fluid for a square-well fluid
✍ Rajat Srivastava; K.N. Khanna πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 396 KB

Self-diffusion coefficients for a dense fluid of particles interacting with a square-well potential employing high temperature approximation have been described. Further, the dependence of the diffusion coefficient and shear viscosity on the excess entropy have been analyzed for a square-well potent

Solution of the Fokker-Planck equation f
Solution of the Fokker-Planck equation for a particle crossing a square well barrier
✍ B. Nowakowski; H.L. Frisch πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 338 KB

The Fokker-Planck equation is solved exactly for a thermalized particle crossing a square well barrier. The Laplace transform ( in time ) of the particle density is obtained explicitly, and is evaluated analytically for the long time range. For this time regime the effective barrier width is to the