Levinson's theorem for dissipative systems, or how to count the asymptotically disappearing states
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909791598673920 |
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| author | Alexander, A. Faupin, J. Richard, S. |
| author_facet | Alexander, A. Faupin, J. Richard, S. |
| contents | We consider dissipative Schroedinger operators of the form $H=-Δ+V(x)$ on $L^2(\mathbb R^3)$, with $V(x)$ a complex, bounded and decaying potential with a non-positive imaginary part. We prove a topological version of Levinson's theorem corresponding to an index theorem for the discrete, complex spectrum of $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12799 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Levinson's theorem for dissipative systems, or how to count the asymptotically disappearing states Alexander, A. Faupin, J. Richard, S. Mathematical Physics Spectral Theory We consider dissipative Schroedinger operators of the form $H=-Δ+V(x)$ on $L^2(\mathbb R^3)$, with $V(x)$ a complex, bounded and decaying potential with a non-positive imaginary part. We prove a topological version of Levinson's theorem corresponding to an index theorem for the discrete, complex spectrum of $H$. |
| title | Levinson's theorem for dissipative systems, or how to count the asymptotically disappearing states |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2509.12799 |