Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathcal{PT}$-symmetric strings   We study both analytically and numerically the spectrum of inhomogeneous
strings with $\mathcal{PT}$-symmetric density. We discuss an exactly solvable
model of $\mathcal{PT}$-symmetric string which is isospectral to the uniform
string; for more general strings, we calculate exactly the sum rules $Z(p)
\equiv \sum_{n=1}^\infty 1/E_n^p$, with $p=1,2,\dots$ and find explicit
expressions which can be used to obtain bounds on the lowest eigenvalue. A
detailed numerical calculation is carried out for two non-solvable models
depending on a parameter, obtaining precise estimates of the critical values
where pair of real eigenvalues become complex.

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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: q-fin