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The regularized trace of the heat kernel of a one-dimensional Schr\"odingeroperator with a singular two-particle contact interaction being of Lieb-Linigertype is considered. We derive a complete small-time asymptotic expansion in(fractional) powers of the time, $t$. Most importantly, we do not invokestandard parametrix constructions for the heat kernel. Instead, we first derivethe large-energy expansion of the regularized trace of the resolvent for theconsidered operator. Then, we exploit that the resolvent may be obtained by aLaplace transformation of the heat semi-group, and an application of a suitableinverse Watson lemma eventually yields the small-$t$ asymptotic expansion ofthe heat-kernel trace.

An asymptotic expansion of the trace of the heat kernel of a singular two-particle contact interaction in one dimension