The regularized trace of the heat kernel of a one-dimensional Schrödinger 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 delivers the small-t asymptotic expansion of the heat-kernel trace.
CITATION STYLE
Egger, S. (2020). An asymptotic expansion of the trace of the heat kernel of a singular two-particle contact interaction in one-dimension. In Operator Theory: Advances and Applications (Vol. 281, pp. 127–152). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-44097-8_6
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