# Diffusion in a logarithmic potential: scaling and selection in the approach to equilibrium

@article{Hirschberg2012DiffusionIA, title={Diffusion in a logarithmic potential: scaling and selection in the approach to equilibrium}, author={Ori Hirschberg and David Mukamel and Gunter M. Schutz}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2012}, volume={2012}, pages={02001} }

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 () and a subdiffusive () length scale…

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