Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A criterion for the reality of the spectrum of PT symmetric Schroedinger
  operators with complex-valued periodic potentials   Consider in $L^2(\R)$ the \Sc operator family $H(g):=-d^2_x+V_g(x)$ depending
on the real parameter $g$, where $V_g(x)$ is a complex-valued but $PT$
symmetric periodic potential. An explicit condition on $V$ is obtained which
ensures that the spectrum of $H(g)$ is purely real and band shaped;
furthermore, a further condition is obtained which ensures that the spectrum
contains at least a pair of complex analytic arcs.

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The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
16
The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph