Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenvalue splitting for a system of Schr\"odinger operators with an
  energy-level crossing   We study the asymptotic distribution of the eigenvalues of a one-dimensional
two-by-two semiclassical system of coupled Schr\"odinger operators in the
presence of two potential wells and with an energy-level crossing. We provide
Bohr-Sommerfeld quantization condition for the eigenvalues of the system on any
energy-interval above the crossing and give precise asymptotics in the
semiclassical limit $h\to 0^+$. In particular, in the symmetric case, the
eigenvalue splitting occurs and we prove that the splitting is of polynomial
order $h^{\frac32}$ and that the main term in the asymptotics is governed by
the area of the intersection of the two classically allowed domains.

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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
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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: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph