Simple generalization of Kramers theory to finite barrier height in spatial diffusion regime

• Published in: Physics letters. A Vol. 382; no. 32; pp. 2103 - 2107
• Main Author: Bai, Zhan-Wu
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 17-08-2018
• Subjects: Cubic potential; Escape rate; Finite barrier; Kramers theory; Finite barrier; Escape rate; Cubic potential; Kramers theory
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2018.05.036

•The Kramers theory in spatial diffusion regime is simply generalized to finite barrier.•Concept of metastable equilibrium state is proposed, current and population are modified.•Local frequency in original theory is replaced by a nonlocal one, current is modified.•The modified Kramers theory is exemplified by a cubic metastable potential case.
Motivated by the escape process at low reduced barrier heights (measured in units of kBT) is still a stationary one, the Kramers theoretical method in spatial diffusion regime should be applicable to this process. The Kramers theory is generalized to finite barrier height in a simple manner. The integration constant is redetermined by introducing metastable equilibrium state concept and continuous condition of the probability at the joint point of the potential barrier and potential well. The parabolic barrier with local frequency is replaced by a parabolic barrier with nonlocal frequency. The modified Kramers theory is confirmed by a cubic potential case. The maximal relative error in the spatial diffusion regime is less than 3% for the applied parameters.