Generalized Einstein Relation for Brownian Motion in Tilted Periodic Potential
Hidetsugu Sakaguchi
TL;DR
This paper investigates a generalized Einstein relation for Brownian motion in tilted periodic potentials, comparing the exact diffusion constant with the approximation, especially in regimes with stepwise motion.
Contribution
It introduces a generalized Einstein relation applicable to Brownian motion in tilted potentials and assesses its accuracy against exact diffusion constants.
Findings
Generalized Einstein relation closely matches exact diffusion in certain regimes.
Approximation is valid where Brownian motion shows stepwise behavior.
Provides insights into diffusion in tilted periodic systems.
Abstract
A generalized Einstein relation is studied for Brownian motion in a tilted potential. The exact form of the diffusion constant of the Brownian motion is compared with the generalized Einstein relation. The generalized Einstein relation is a good approximation in a parameter range where the Brownian motion exhibits stepwise motion.
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