The Friedrichs-Lee Model and Its Singular Coupling Limit †
Abstract
:1. Introduction
- No square-integrable form factor implementing an exponential decay of the survival probability of exists, since is in the domain of the Hamiltonian [3,4]. An exponential decay can be formally obtained e.g. in a one-dimensional setting , with and , but such a form factor obviously fails to be square-integrable;
- The standard choices of parameters in waveguide QED (see e.g., [5]) arem being the effective photon mass; the form factor g fails to be square-integrable because of its behaviour at large momenta (UV divergence).
2. Singular Coupling
- ;
- ;
- ,
3. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Coupling | ||||
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∞ | ∞ |
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Lonigro, D.; Facchi, P.; Ligabò, M. The Friedrichs-Lee Model and Its Singular Coupling Limit. Proceedings 2019, 12, 17. https://doi.org/10.3390/proceedings2019012017
Lonigro D, Facchi P, Ligabò M. The Friedrichs-Lee Model and Its Singular Coupling Limit. Proceedings. 2019; 12(1):17. https://doi.org/10.3390/proceedings2019012017
Chicago/Turabian StyleLonigro, Davide, Paolo Facchi, and Marilena Ligabò. 2019. "The Friedrichs-Lee Model and Its Singular Coupling Limit" Proceedings 12, no. 1: 17. https://doi.org/10.3390/proceedings2019012017
APA StyleLonigro, D., Facchi, P., & Ligabò, M. (2019). The Friedrichs-Lee Model and Its Singular Coupling Limit. Proceedings, 12(1), 17. https://doi.org/10.3390/proceedings2019012017