Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An operator-theoretical proof for the second-order phase transition in
  the BCS-Bogoliubov model of superconductivity (final version)   We show that the transition from a normal conducting state to a
superconducting state is a second-order phase transition in the BCS-Bogoliubov
model of superconductivity from the viewpoint of operator theory. Here we have
no magnetic field. Moreover we obtain the exact and explicit expression for the
gap in the specific heat at constant volume at the transition temperature. To
this end, we have to differentiate the thermodynamic potential with respect to
the temperature two times. Since there is the solution to the BCS-Bogoliubov
gap equation in the form of the thermodynamic potential, we have to
differentiate the solution with respect to the temperature two times.
Therefore, we need to show that the solution to the BCS-Bogoliubov gap equation
is differentiable with respect to the temperature two times as well as its
existence and uniqueness. We carry out its proof on the basis of fixed point
theorems.

31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas