Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete Spectrum of a Model Operator Related to Three-Particle Discrete
  Schr\"{o}dinger Operators   A model operator $H_\mu,$ $\mu>0$ associated to a system of three particles
on the three-dimensional lattice $ \mathbb{Z}^3$ that interact via nonlocal
pair potentials is considered. We study the case where the parameter function
$w$ has a special form with the non degenerate minimum at the $n, n>1$ points
of the six-dimensional torus $\mathbb{T}^6.$ If the associated Friedrichs model
has a zero energy resonance, then we prove that the operator $H_\mu$ has
infinitely many negative eigenvalues accumulating at zero and we obtain an
asymptotics for the number of eigenvalues of $H_\mu$ lying below $z,$ $z<0$ as
$z\to -0.$

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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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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: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: funct-an