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@ARTICLE{Hirschberg:20049,
      author       = {Hirschberg, O. and Mukamel, D. and Schütz, G.M.},
      title        = {{D}iffusion in a logarithmic potential: scaling and
                      selection in the approach to equilibrium},
      journal      = {Journal of statistical mechanics: theory and experiment},
      volume       = {2012},
      issn         = {1742-5468},
      address      = {Bristol},
      publisher    = {IOP Publ.},
      reportid     = {PreJuSER-20049},
      pages        = {P02001},
      year         = {2012},
      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).},
      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.},
      keywords     = {J (WoSType)},
      cin          = {ICS-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)ICS-2-20110106},
      pnm          = {BioSoft: Makromolekulare Systeme und biologische
                      Informationsverarbeitung},
      pid          = {G:(DE-Juel1)FUEK505},
      shelfmark    = {Mechanics / Physics, Mathematical},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000300904900002},
      doi          = {10.1088/1742-5468/2012/02/P02001},
      url          = {https://juser.fz-juelich.de/record/20049},
}