Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the spectral gap of higher-dimensional Schr\"odinger operators on
  large domains   We study the asymptotic behaviour of the spectral gap of Schr\"odinger
operators in two and higher dimensions and in a limit where the volume of the
domain tends to infinity. Depending on properties of the underlying potential,
we will find different asymptotic behaviours of the gap. In some cases the gap
behaves as the gap of the free Dirichlet Laplacian and in some cases it does
not.

9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat