Equations for the distributions of functionals of a random-walk trajectory in an inhomogeneous medium

Journal Article · Sun Jan 15 04:00:00 EST 2012 · Journal of Experimental and Theoretical Physics

DOI:https://doi.org/10.1134/S1063776111150106· OSTI ID:22027933

Based on the random-trap model and using the mean-field approximation, we derive an equation that allows the distribution of a functional of the trajectory of a particle making random walks over inhomogeneous-lattice site to be calculated. The derived equation is a generalization of the Feynman-Kac equation to an inhomogeneous medium. We also derive a backward equation in which not the final position of the particle but its position at the initial time is used as an independent variable. As an example of applying the derived equations, we consider the one-dimensional problem of calculating the first-passage time distribution. We show that the average first-passage times for homogeneous and inhomogeneous media with identical diffusion coefficients coincide, but the variance of the distribution for an inhomogeneous medium can be many times larger than that for a homogeneous one.

• OSTI ID: 22027933
• Journal Information: Journal of Experimental and Theoretical Physics, Journal Name: Journal of Experimental and Theoretical Physics Journal Issue: 1 Vol. 114; ISSN JTPHES; ISSN 1063-7761
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
DIFFERENTIAL EQUATIONS
DIFFUSION
FUNCTIONALS
GRAPH THEORY
MEAN-FIELD THEORY
ONE-DIMENSIONAL CALCULATIONS
RANDOMNESS
TRAJECTORIES
TRAPS