Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral asymptotics and Lam\'e spectrum for coupled particles in
  periodic potentials   We make two observations on the motion of coupled particles in a periodic
potential. Coupled pendula, or the space-discretized sine-Gordon equation is an
example of this problem. Linearized spectrum of the synchronous motion turns
out to have a hidden asymptotic periodicity in its dependence on the energy;
this is the gist of the first observation. Our second observation is the
discovery of a special property of the purely sinusoidal potentials: the
linearization around the synchronous solution is equivalent to the classical
Lam\`e equation. As a consequence, {\it all but one instability zones of the
linearized equation collapse to a point for the one-harmonic potentials}. This
provides a new example where Lam\'e's finite zone potential arises in the
simplest possible setting.

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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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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: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: eess