2019/12/05 by Rohan Maniar, Maniar, Rohan, A. Bhattacharyay +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1912.11529
9 pages and 15 figures. More clarifications on the method are given in this version along with some corrections in the text
openalex publication_date 2019/12/05 · arxiv created 2020/08/26 · arxiv updated 2020/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we develop a random walk model on lattice for coordinate dependent diffusion at constant temperature in contact with a heat bath. We employ here a coordinate dependent waiting time of the random walker to make the diffusivity coordinate dependent. The presence of a confining conservative force is modeled by appropriately breaking the isotropy of the jumps of the random walker to its nearest neighbors. We show that the equilibrium is characterized by the position distribution which is of modified Boltzmann form. We also show that, in such systems with coordinate dependent diffusivity, the modified Boltzmann distribution correctly captures the transition over a potential barrier as opposed to the Boltzmann distribution.