Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbation Theory for the Periodic Multidimensional Schrodinger
  Operator and the Bethe-Sommerfeld Conjecture   In this paper we obtain asymptotic formulas of arbitrary order for the Bloch
eigenvalue and the Bloch function of the periodic Schrodinger operator of
arbitrary dimension, when corresponding quasimomentum lies near a diffraction
hyperplane. Besides, writing the asymptotic formulas for the Bloch eigenvalue
and the Bloch function, when corresponding quasimomentum lies far from the
diffraction hyperplanes, obtained in my previous papers in improved and
enlarged form, we obtain the complete perturbation theory for the
multidimensional Schrodinger operator with a periodic potential. Moreover, we
estimate the measure of the isoenergetic surfaces in the high energy region
which implies the validity of the Bethe-Sommerfeld conjecture for arbitrary
dimension and arbitrary lattice.

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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph