Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems
Mathematical Physics
2025-11-24 v2 Functional Analysis
math.MP
Probability
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.
Cite
@article{arxiv.2511.02867,
title = {Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems},
author = {Benjamin Hinrichs and Steffen Polzer},
journal= {arXiv preprint arXiv:2511.02867},
year = {2025}
}
Comments
29 pages, 1 figure