Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbation Theory for PT-Symmetric Sinusoidal Optical Lattices at the
  Symmetry-Breaking Threshold   The $PT$ symmetric potential $V_0[\cos(2\pi x/a)+i\lambda\sin(2\pi x/a)]$ has
a completely real spectrum for $\lambda\le 1$, and begins to develop complex
eigenvalues for $\lambda>1$. At the symmetry-breaking threshold $\lambda=1$
some of the eigenvectors become degenerate, giving rise to a Jordan-block
structure for each degenerate eigenvector. In general this is expected to give
rise to a secular growth in the amplitude of the wave. However, it has been
shown in a recent paper by Longhi, by numerical simulation and by the use of
perturbation theory, that for an initial wave packet this growth is suppressed,
giving instead a constant maximum amplitude. We revisit this problem by
developing the perturbation theory further. We verify that the results found by
Longhi persist to second order, and with different input wave packets we are
able to see the seeds in perturbation theory of the phenomenon of birefringence
first discovered by Makris et al.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: math
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th