Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermal effects in gravitational Hartree systems   We consider the non-relativistic Hartree model in the gravitational case,
i.e. with attractive Coulomb-Newton interaction. For a given mass, we construct
stationary states with non-zero temperature by minimizing the corresponding
free energy functional. It is proved that minimizers exist if and only if the
temperature of the system is below a certain threshold(possibly infinite),
which itself depends on the specific choice of the entropy functional. We also
investigate whether the corresponding minimizers are mixed or pure quantum
states and characterize a positive critical temperature above which mixed
states appear.

37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat