Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact diffusion coefficient of self-gravitating Brownian particles in
  two dimensions   We derive the exact expression of the diffusion coefficient of a
self-gravitating Brownian gas in two dimensions. Our formula generalizes the
usual Einstein relation for a free Brownian motion to the context of
two-dimensional gravity. We show the existence of a critical temperature T_{c}
at which the diffusion coefficient vanishes. For T<T_{c} the diffusion
coefficient is negative and the gas undergoes gravitational collapse. This
leads to the formation of a Dirac peak concentrating the whole mass in a finite
time. We also stress that the critical temperature T_{c} is different from the
collapse temperature T_{*} at which the partition function diverges. These
quantities differ by a factor 1-1/N where N is the number of particles in the
system. We provide clear evidence of this difference by explicitly solving the
case N=2. We also mention the analogy with the chemotactic aggregation of
bacteria in biology, the formation of ``atoms'' in a two-dimensional (2D)
plasma and the formation of dipoles or supervortices in 2D point vortex
dynamics.

26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga