A Gutzwiller trace formula for singular potentials
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912607502336000 |
|---|---|
| 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 |