Abstract
We introduce a functional version of the Kato one-parameter regularization for constructing a dynamical semigroup generator of a relative bound-one perturbation. As an example of an application, we consider a regularization based on a boson-number cutoff.
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Acknowledgments
One of the authors (V. A. Z.) is grateful to the Department of Mathematics of the University of Auckland and to Tom ter Elst for the warm hospitality. He is also thankful to Alessandro Giuliani for a fruitful discussion of the boson open systems, which motivated him to consider a revision of the standard Kato regularization. The authors are thankful to a referee for the remarks and suggestions.
Funding
The visits of V. A. Zagrebnov to the University of Auckland in 2015 and 2016 were supported by the EU Marie Curie IRSES program (Project “AOS,” No. 318910) and the Marsden Fund Council from government funding administered by the Royal Society of New Zealand.
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ter Elst, A.F.M., Zagrebnov, V.A. Construction of dynamical semigroups by a functional regularization à la Kato. Theor Math Phys 204, 875–895 (2020). https://doi.org/10.1134/S004057792007003X
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DOI: https://doi.org/10.1134/S004057792007003X