Abstract
We study the spectrum of the spin-boson model with two photons in \({\mathbb {R}}^d\) for arbitrary coupling \(\alpha >0\). It is shown that the discrete spectrum is finite and the essential spectrum consists of a half-line, the bottom of which is a unique zero of a simple Nevanlinna function. Besides the simplicity and more abstract nature of our approach, the main novelty is the achievement of these results under minimal regularity conditions on the photon dispersion and the coupling function.
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Acknowledgements
The author is grateful to Prof. A.V. Sobolev for fruitful discussions, reading the preliminary version of this manuscript and making useful suggestions and thanks the Department of Mathematics at University College London for the kind hospitality. Thanks also go to the anonymous referee for a number of useful suggestions. The financial support of the Swiss National Science Foundation, SNF, through the Early Postdoc.Mobility grant No. 168723 is gratefully acknowledged.
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Communicated by Jan Derezinski.
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Ibrogimov, O.O. Spectral Analysis of the Spin-Boson Hamiltonian with Two Photons for Arbitrary Coupling. Ann. Henri Poincaré 19, 3561–3579 (2018). https://doi.org/10.1007/s00023-018-0725-z
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DOI: https://doi.org/10.1007/s00023-018-0725-z