Feynman–Kac equations for reaction and diffusion processes. (15th March 2018)

• Record Type: Journal Article
• Authors: Hou, Ru; Deng, Weihua
• Is Part Of: Journal of physics. Volume 51:Number 15(2018)
• Publication Date: 2018-03-15
• Subjects: Feynman–Kac equation -- reaction and diffusion process -- distribution of functional; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aab1af
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: This paper provides a theoretical framework for deriving the forward and backward Feynman–Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman–Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.