Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp asymptotics for the Neumann Laplacian with variable magnetic field
  : case of dimension 2   The aim of this paper is to establish estimates of the lowest eigenvalue of
the Neumann realization of $(i\nabla+B\textbf{A})^2$ on an open bounded subset
of $\mathbb{R}^2$ $\Omega$ with smooth boundary as $B$ tends to infinity. We
introduce a "magnetic" curvature mixing the curvature of $\partial\Omega$ and
the normal derivative of the magnetic field and obtain an estimate analogous
with the one of constant case. Actually, we give a precise estimate of the
lowest eigenvalue in the case where the restriction of magnetic field to the
boundary admits a unique minimum which is non degenerate. We also give an
estimate of the third critical field in Ginzburg-Landau theory in the variable
magnetic field case.

15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio