Approach to equilibrium in adiabatically evolving potentials

Samanta, H S. ; Bhattacharjee, J. K. ; Ramaswamy, R. (2004) Approach to equilibrium in adiabatically evolving potentials Physical Review E, 69 (5). 056114_1-056114_5. ISSN 1063-651X

[img]
Preview
PDF - Publisher Version
155kB

Official URL: http://pre.aps.org/abstract/PRE/v69/i5/e056114

Related URL: http://dx.doi.org/10.1103/PhysRevE.69.056114

Abstract

For a potential function (in one dimension) which evolves from a specified initial form Vi(x) to a different Vf(x) asymptotically, we study the evolution, in an overdamped dynamics, of an initial probability density to its final equilibrium. There can be unexpected effects that can arise from the time dependence. We choose a time variation of the form V(x,t)=Vf(x)+(Vi-Vf)e-λt. For a Vf(x), which is double welled and a Vi(x) which is simple harmonic, we show that, in particular, if the evolution is adiabatic, this results in a decrease in the Kramers time characteristic of Vf(x). Thus the time dependence makes diffusion over a barrier more efficient. There can also be interesting resonance effects when Vi(x) and Vf(x) are two harmonic potentials displaced with respect to each other that arise from the coincidence of the intrinsic time scale characterizing the potential variation and the Kramers time. Both these features are illustrated through representative examples.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:2616
Deposited On:08 Oct 2010 09:01
Last Modified:16 May 2016 13:34

Repository Staff Only: item control page