Approach to equilibrium in adiabatically evolving potentials

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dc.creatorSamanta, H. S.
dc.creatorBhattacharjee, J. K.
dc.creatorRamaswamy, R.
dc.date2004-12-09
dc.date.accessioned2026-07-07T03:02:34Z
dc.date.available2026-07-07T03:02:34Z
dc.descriptionFor a potential function (in one dimension) which evolves from a specified initial form $V_{i}(x)$ to a different $V_{f}(x)$ asymptotically, we study the evolution, in an overdamped dynamics, of an initial probability density to its final equilibeium.There can be unexpected effects that can arise from the time dependence. We choose a time variation of the form $V(x,t)=V_{f}(x)+(V_{i}-V_{f})e^{-λt}$. For a $V_{f}(x)$, which is double welled and a $V_{i}(x)$ which is simple harmonic, we show that, in particular, if the evolution is adiabatic, the results in a decrease in the Kramers time characteristics of $V_{f}(x)$. Thus the time dependence makes diffusion over a barrier more efficient. There can also be interesting resonance effects when $V_{i}(x)$ and $V_{f}(x)$ are two harmonic potentials displaced with respect to each other that arise from the coincidence of the intrinsic time scale characterising the potential variation and the Kramers time.
dc.descriptionThis paper contains 5 pages
dc.identifierhttps://arxiv.org/abs/cond-mat/0412215
dc.identifierhttp://arxiv.org/abs/cond-mat/0412215
dc.identifierPRE 69,056114(2004)
dc.identifierdoi:10.1103/PhysRevE.69.056114
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/25441
dc.subjectStatistical Mechanics
dc.titleApproach to equilibrium in adiabatically evolving potentials
dc.typetext

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