A Gutzwiller trace formula for singular potentials
Analysis of PDEs
2025-09-29 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
The Gutzwiller trace formula relates the asymptotic spacing of quantum-mechanical energy levels in the semiclassical limit to the dynamics of periodic classical particle trajectories. We generalize this result to the case of non-smooth potentials, for which there is partial reflection of energy from derivative discontinuities of the potential. It is the periodic trajectories of an associated branching dynamics that contribute to the trace asymptotics in this more general setting; we obtain a precise description of their contribution.
Cite
@article{arxiv.2509.05220,
title = {A Gutzwiller trace formula for singular potentials},
author = {Jared Wunsch and Mengxuan Yang and Yuzhou Joey Zou},
journal= {arXiv preprint arXiv:2509.05220},
year = {2025}
}
Comments
added Lemmas 2.12 and 2.13 on finiteness of flowout. 55 pages, comments are welcome