Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 146, Issue 4, Pages 762-773Publisher
SPRINGER
DOI: 10.1007/s10955-012-0418-9
Keywords
Brownian motion; Stochastic differential equations; Smoluchowski-Kramers approximation; Einstein mobility-diffusion relation
Categories
Funding
- University of Arizona
- NSF [DMS 1009508]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1009508] Funding Source: National Science Foundation
Ask authors/readers for more resources
We consider the dynamics of systems with arbitrary friction and diffusion. These include, as a special case, systems for which friction and diffusion are connected by Einstein fluctuation-dissipation relation, e. g. Brownian motion. We study the limit where friction effects dominate the inertia, i.e. where the mass goes to zero (Smoluchowski-Kramers limit). Using the Ito stochastic integral convention, we show that the limiting effective Langevin equations has different drift fields depending on the relation between friction and diffusion. Alternatively, our results can be cast as different interpretations of stochastic integration in the limiting equation, which can be parametrized by alpha is an element of R. Interestingly, in addition to the classical Ito (alpha = 0), Stratonovich (alpha = 0.5) and anti-Ito (alpha = 1) integrals, we show that position-dependent alpha = alpha(x), and even stochastic integrals with alpha is not an element of [0, 1] arise. Our findings are supported by numerical simulations.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available