Exact solution of Kramers' problem for piecewise parabolic potential profiles

✍ Scribed by A.N. Malakhov; A.L. Pankratov

• Book ID: 103896162
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 651 KB
• Volume: 229
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(95)00395-9

✦ Synopsis

This paper presents a general procedure for deducing exact time characteristics of Brownian diffusion in the high damping limit in piecewise parabolic potential profiles.

Our approach to solve this problem is based on the Laplace transform method for obtaining the desired time characteristics. For some concrete examples of piecewise parabolic profiles exact values of metastable state decay times and bistable system relaxation times are found. These results are valid for any height of the potential barrier and coincide with Kramers' results for a high potential barrier. Conditions for the validity of Kramers' formula are also derived.