A Gutzwiller trace formula for singular potentials

Fuente: arXiv
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Main Authors: Wunsch, Jared, Yang, Mengxuan, Zou, Yuzhou Joey
Format: Preprint
Published: 2025
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author Wunsch, Jared
Yang, Mengxuan
Zou, Yuzhou Joey
author_facet Wunsch, Jared
Yang, Mengxuan
Zou, Yuzhou Joey
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_05220
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Gutzwiller trace formula for singular potentials
Wunsch, Jared
Yang, Mengxuan
Zou, Yuzhou Joey
Analysis of PDEs
Mathematical Physics
Spectral Theory
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.
title A Gutzwiller trace formula for singular potentials
topic Analysis of PDEs
Mathematical Physics
Spectral Theory
url https://arxiv.org/abs/2509.05220