Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Method of studying the Bogoliubov-de Gennes equations for the
  superconducting vortex lattice state   In this paper, we present a method to construct the eigenspace of the
normal-state electrons moving in a 2D square lattice in presence of a
perpendicular uniform magnetic field which imposes (quasi)-periodic boundary
conditions for the wave functions in the magnetic unit cell. An exact unitary
transformations are put forward to correlate the discrete eigenvectors of the
2D electrons with those of the Harper's equation. The cyclic-tridiagonal matrix
associated with the Harper's equation is then tridiagonalized by another
unitary transformation. The obtained eigenbasis is utilized to expand the
Bogoliubov-de Gennes equations for the superconducting vortex lattice state,
which showing the merit of our method in studying the large-sized system. To
test our method, we have applied our results to study the vortex lattice state
of an s-wave superconductor.

31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th