Overdamped limit and inverse-friction expansion for Brownian motion in an inhomogeneous medium
Abstract
We revisit the problem of the overdamped (large-friction) limit of the Brownian dynamics in an inhomogeneous medium characterized by a position-dependent friction coefficient and a multiplicative noise (local temperature) in one-dimensional space. Starting from the Kramers equation and analyzing it through the expansion in terms of eigenfunctions of a quantum harmonic oscillator, we derive analytically the corresponding Fokker-Planck equation in the overdamped limit. The result is fully consistent with the previous finding by Sancho, San Miguel, and Dürr [J. Stat. Phys. 28, 291 (1982)]. Our method allows us to generalize the Brinkman's hierarchy, and thus it would be straightforward to obtain higher-order corrections in a systematic inverse-friction expansion without any assumption. Our results are confirmed by numerical simulations for simple examples.
Read the paper
Related studies
- Quantum dots: synthesis, bioapplications, and toxicity
- A Guide to In Silico Drug Design
- Quantum Computing for Healthcare: A Review
- Automated in Silico Design of Homogeneous Catalysts
- Identification of Novel 3-Hydroxy-pyran-4-One Derivatives as Potent HIV-1 Integrase Inhibitors Using in silico Structure-Based Combinatorial Library Design Approach
- In silico structural elucidation of RNA-dependent RNA polymerase towards the identification of potential Crimean-Congo Hemorrhagic Fever Virus inhibitors
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.