Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nodal sets of magnetic Schroedinger operators of Aharonov-Bohm type and
  energy minimizing partitions   In this paper we consider a stationary Schroedinger operator in the plane, in
presence of a magnetic field of Aharonov-Bohm type with semi-integer
circulation. We analyze the nodal regions for a class of solutions such that
the nodal set consists of regular arcs, connecting the singular points with the
boundary. In case of one magnetic pole, which is free to move in the domain,
the nodal lines may cluster dissecting the domain in three parts. Our main
result states that the magnetic energy is critical (with respect to the
magnetic pole) if and only if such a configuration occurs. Moreover the nodal
regions form a minimal 3-partition of the domain (with respect to the real
energy associated to the equation), the configuration is unique and depends
continuously on the data. The analysis performed is related to the notion of
spectral minimal partition introduced in [20]. As it concerns eigenfunctions,
we similarly show that critical points of the Rayleigh quotient correspond to
multiple clustering of the nodal lines.

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The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs