Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusion in a logarithmic potential: scaling and selection in the
  approach to equilibrium   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 ~
\sqrt{t}) and a subdiffusive (x >> \sqrt{t}) length scales, 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.

35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org