Time asymptotics of e(-ith(kappa)) for analytic matrices and analytic perturbation theory
- In quantum mechanics the temporal decay of certain resonance states is associated with an effective time evolution e(-ith(kappa)), where h(.) is an analytic family of non-self-adjoint matrices. In general the corresponding resonance states do not decay exponentially in time. Using analytic perturbation theory, we derive asymptotic expansions for e(-ith(kappa)), simultaneously in the limits kappa -> 0 and t -> infinity, where the corrections with respect to pure exponential decay have uniform bounds in one complex variable kappa(2)t.
In the Appendix we briefly review analytic perturbation theory, replacing the classical reference to the 1920 book of Knopp [Funktionentheorie II, Anwendungen und Weiterfuhrung der allgemeinen Theorie, Sammlung Goschen, Vereinigung wissenschaftlicher Verleger Walter de Gruyter, 1920] and its terminology by standard modern references. This might be of independent interest.
MetadatenAuthor details: | Markus KleinGND, Juliane Rama |
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DOI: | https://doi.org/10.3233/ASY-141226 |
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ISSN: | 0921-7134 |
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ISSN: | 1875-8576 |
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Title of parent work (English): | Asymptotic analysis |
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Publisher: | IOS Press |
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Place of publishing: | Amsterdam |
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Publication type: | Article |
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Language: | English |
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Year of first publication: | 2014 |
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Publication year: | 2014 |
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Release date: | 2017/03/27 |
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Tag: | Fermi golden rule; analytic perturbation theory; exponential decay; long-time corrections; resonances |
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Volume: | 89 |
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Issue: | 3-4 |
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Number of pages: | 45 |
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First page: | 189 |
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Last Page: | 233 |
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Funding institution: | Deutsche Forschungsgemeinschaft (DFG) [KL 800/2-2, 2020/3-1];
Universitat Potsdam; Centre Interfacultaire Bernoulli; Department of
Mathematics at the University of Virginia |
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Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
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Peer review: | Referiert |
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