Journal Article

PreJuSER-20049

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Diffusion in a logarithmic potential: scaling and selection in the approach to equilibrium

Hirschberg, O.FZJ* ; Mukamel, D.FZJ* ; Schütz, G. M.FZJ*

2012
IOP Publ. Bristol

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Please use a persistent id in citations: doi:10.1088/1742-5468/2012/02/P02001

Abstract: The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed study of the approach of such systems to equilibrium via a scaling analysis is carried out, revealing three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x similar to root t) and a subdiffusive (x << root t) length scale, respectively; (ii) the scaling exponents and scaling functions corresponding to both regimes are selected by the initial condition; and (iii) this dependence on the initial condition manifests a 'phase transition' from a regime in which the scaling solution depends on the initial condition to a regime in which it is independent of it. The selection mechanism which is found has many similarities to the marginal stability mechanism, which has been widely studied in the context of fronts propagating into unstable states. The general scaling forms are presented and their practical and theoretical applications are discussed.

Keyword(s): J ; stochastic processes (theory) (auto) ; diffusion (auto)

Note: We thank A Amir, A Bar, O Cohen, N Davidson, J-P Eckmann, M R Evans, and T Sadhu for useful discussions and comments on the paper. This work was supported by the Israel Science Foundation (ISF).

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Contributing Institute(s):

1. Theorie der weichen Materie und Biophysik (ICS-2)

Research Program(s):

1. BioSoft: Makromolekulare Systeme und biologische Informationsverarbeitung (P45)

Appears in the scientific report 2012

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Database coverage:
; Current Contents - Social and Behavioral Sciences ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index Expanded ; Thomson Reuters Master Journal List ; Web of Science Core Collection

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