Diffusion under a flat potential with time dependent sink
Diwaker, Anirudhha Chakraborty
TL;DR
This paper provides exact solutions to the Smoluchowski equation for a free particle with a time-dependent sink, enabling the determination of the probability distribution at all positions from the distribution at the origin.
Contribution
It introduces an exact analytical method to solve the Smoluchowski equation with a time-dependent sink for various special cases.
Findings
Exact solutions for the probability distribution with a time-dependent sink
Method to derive full distribution from the origin distribution
Applicable to multiple special cases of the sink function
Abstract
The Smoluchowski equation for a free particle with a time dependent sink is solved exactly for many special cases. In this method by knowing the probability distribution at the origin P(0,t), one may derive the probability distribution at all positions i.e. P(x,t)
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Taxonomy
TopicsStatistical Mechanics and Entropy · Theoretical and Computational Physics · Cold Atom Physics and Bose-Einstein Condensates