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arXiv · 2511.02867

Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems

Benjamin Hinrichs·Steffen Polzer
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Abstract

We study the behavior of a probability measure near the bottom of its support in terms of time averaged quotients of its Laplace transform. We discuss how our results are connected to both rank-one perturbation theory as well as renewal theory. We further apply our results in order to derive criteria for the existence and non-existence of ground states for a finite dimensional quantum system coupled to a bosonic field.

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Benjamin Hinrichs, Steffen Polzer. 2025-11-03. Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems. https://arxiv.org/abs/2511.02867

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