Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Floquet Method for $PT$-symmetric Periodic Potentials   By the general theory of $PT$-symmetric quantum systems, their energy levels
are either real or occur in complex-conjugate pairs, which implies that the
secular equation must be real. However, for periodic potentials it is by no
means clear that the secular equation arising in the Floquet method is indeed
real, since it involves two linearly independent solutions of the Schr\"odinger
equation. In this brief note we elucidate how that reality can be established.

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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-th