Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Origin of branch points in the spectrum of PT-symmetric periodic
  potentials   There exists multiple branch points in the energy spectrum for some
\emph{PT}-symmetric periodic potentials, where the real eigenvalues turn into
complex ones. By studying the transmission amplitude for a localized complex
potential, we elucidate the physical origin of the breakdown of perturbation
method and Born approximation. Mostly importantly, we derive an analytic
criteria to determine why, when and where the bifurcation will occur.

29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn