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
Eigenvalues of the Fokker—Planck and BGK operators for a double-well potential
✍ Scribed by K. Voigtlaender; H. Risken
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 389 KB
- Volume
- 105
- Category
- Article
- ISSN
- 0009-2614
No coin nor oath required. For personal study only.
✦ Synopsis
Eigenvalues of the Fokker-Planck
and BGK operators for a d2x2/2 + da4/4 double-well potential are ulculated by the matrix continued-fraction method. A dependence of the eigenvalues on the friction constant or coupbng strength is shown for the lowest non-zero real eigenvalue and for some higher, generally complex eigenvalues.
📜 SIMILAR VOLUMES
In this paper, the periodic and the Dirichlet problems for the Schrödinger operator -(d 2 /dx 2 )+V are studied for singular, complex-valued potentials V in the Sobolev space H -a per [0, 1] (0 [ a < 1). The following results are shown: (1) The periodic spectrum consists of a sequence (l k ) k \ 0