Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of eigenvalue sums when some turning points are complex   Recent work has shown a deep connection between semilocal approximations in
density functional theory and the asymptotics of the sum of the WKB
semiclassical expansion for the eigenvalues. However, all examples studied to
date have potentials with only real classical turning points. But systems with
complex turning points generate subdominant terms beyond those in the WKB
series. The simplest case is a pure quartic oscillator. We show how to
generalize the asymptotics of eigenvalue sums to include subdominant
contributions to the sums, if they are known for the eigenvalues. These
corrections to WKB greatly improve accuracy for eigenvalue sums, especially for
many levels. We obtain further improvements to the sums through
hyperasymptotics. For the lowest level, our summation method has error below $2
\times 10^{-4}$. For the sum of the lowest 10 levels, our error is less than
$10^{-22}$. We report all results to many digits and include copious details of
the asymptotic expansions and their derivation.

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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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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: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph