TY  - JOUR
AU  - Hirschberg, O.
AU  - Mukamel, D.
AU  - Schütz, G.M.
TI  - Diffusion in a logarithmic potential: scaling and selection in the approach to equilibrium
JO  - Journal of statistical mechanics: theory and experiment
VL  - 2012
SN  - 1742-5468
CY  - Bristol
PB  - IOP Publ.
M1  - PreJuSER-20049
SP  - P02001
PY  - 2012
N1  - 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).
AB  - 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.
KW  - J (WoSType)
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000300904900002
DO  - DOI:10.1088/1742-5468/2012/02/P02001
UR  - https://juser.fz-juelich.de/record/20049
ER  -