Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-Instantons and Exact Results III: Unified Description of the
  Resonances of Even and Odd Anharmonic Oscillators   This is the third article in a series of three papers on the resonance energy
levels of anharmonic oscillators. Whereas the first two papers mainly dealt
with double-well potentials and modifications thereof [see J. Zinn-Justin and
U. D. Jentschura, Ann. Phys. (N.Y.) 313 (2004), pp. 197 and 269], we here focus
on simple even and odd anharmonic oscillators for arbitrary magnitude and
complex phase of the coupling parameter. A unification is achieved by the use
of PT-symmetry inspired dispersion relations and generalized quantization
conditions that include instanton configurations. Higher-order formulas are
provided for the oscillators of degrees 3 to 8, which lead to subleading
corrections to the leading factorial growth of the perturbative coefficients
describing the resonance energies. Numerical results are provided, and
higher-order terms are found to be numerically significant. The resonances are
described by generalized expansions involving intertwined non-analytic
exponentials, logarithmic terms and power series. Finally, we summarize
spectral properties and dispersion relations of anharmonic oscillators, and
their interconnections. The purpose is to look at one of the classic problems
of quantum theory from a new perspective, through which we gain systematic
access to the phenomenologically significant higher-order terms.

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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: gr-qc