Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vortex Lattices and the Bogoliubov-De Gennes Equations   We consider the Bogoliubov-de Gennes equations giving an equivalent
formulation of the BCS theory of superconductivity. We are interested in static
solutions with the magnetic field present. We carefully formulate the equations
in the basis independent form, discuss their general features and isolate key
physical classes of solutions (normal and vortex lattice states) which are the
candidates for the ground state. We prove existence of the normal and vortex
lattice states and stability of the normal states for large temperature or
magnetic fields and their instability for small temperature and small magnetic
fields.

37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin