Equations for the distributions of functionals of a random-walk trajectory in an inhomogeneous medium |
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Authors: | V P Shkilev |
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Institution: | 1.Institute of Surface Chemistry,National Academy of Sciences of Ukraine,Kiev,Ukraine |
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Abstract: | 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. |
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Keywords: | |
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