Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An asymptotic expansion of the trace of the heat kernel of a singular
  two-particle contact interaction in one dimension   The regularized trace of the heat kernel of a one-dimensional Schr\"odinger
operator with a singular two-particle contact interaction being of Lieb-Liniger
type is considered. We derive a complete small-time asymptotic expansion in
(fractional) powers of the time, $t$. Most importantly, we do not invoke
standard parametrix constructions for the heat kernel. Instead, we first derive
the large-energy expansion of the regularized trace of the resolvent for the
considered operator. Then, we exploit that the resolvent may be obtained by a
Laplace transformation of the heat semi-group, and an application of a suitable
inverse Watson lemma eventually yields the small-$t$ asymptotic expansion of
the heat-kernel trace.

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The categories of this paper are: patt-sol
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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: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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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: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: physics