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Unusual scaling behaviour of diffusion in a logarithmic potential
Gunter Schütz
IFF Juelich (Allemagne)
Thursday 27 September 2012 , 10h25
Salle de séminaire du groupe de Physique Statistique

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 is carried out, revealing three surprising features: (i) the dynamics is given by two distinct scaling forms, subdiffusive or diffusive,(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. In the context of DNA denaturation we derive a universal subdiffusive growthof the mean formation time of a unzipped bubble of size $N$ which depends on the strength of the entropic contributionto the Poland-Scheraga free energy of the bubble size in a double-stranded DNA.



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