Self-Adjointness of a Class of Multi-Spin–Boson Models with Ultraviolet Divergences

Lonigro D (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Mathematical Physics Analysis and Geometry Springer Verlag (Germany)

Book Volume: 26

Article Number: 15

Journal Issue: 2

DOI: 10.1007/s11040-023-09457-6

Abstract

We study a class of quantum Hamiltonian models describing a family of N two-level systems (spins) coupled with a structured boson field of positive mass, with a rotating-wave coupling mediated by form factors possibly exhibiting ultraviolet divergences. Spin–spin interactions which do not modify the total number of excitations are also included. Generalizing previous results in the single-spin case, we provide explicit expressions for the self-adjointness domain and the resolvent of these models, both of them carrying an intricate dependence on the spin–field and spin–spin coupling via a family of concatenated propagators. This construction is also shown to be stable, in the norm resolvent sense, under approximations of the form factors via normalizable ones, for example an ultraviolet cutoff.

Authors with CRIS profile

Davide Lonigro

Involved external institutions

University of Bari Aldo Moro / Università degli Studi di Bari Aldo Moro IT Italy (IT)

How to cite

APA:

Lonigro, D. (2023). Self-Adjointness of a Class of Multi-Spin–Boson Models with Ultraviolet Divergences. Mathematical Physics Analysis and Geometry, 26(2). https://doi.org/10.1007/s11040-023-09457-6

MLA:

Lonigro, Davide. "Self-Adjointness of a Class of Multi-Spin–Boson Models with Ultraviolet Divergences." Mathematical Physics Analysis and Geometry 26.2 (2023).

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