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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