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Spin-boson type models analyzed using symmetries

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Spin-boson type models analyzed using symmetries. / Dam, Thomas Norman; Møller, Jacob Schach.

In: Kyoto Journal of Mathematics, Vol. 60, No. 4, 12.2020, p. 1261-1332.

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Dam, TN & Møller, JS 2020, 'Spin-boson type models analyzed using symmetries', Kyoto Journal of Mathematics, vol. 60, no. 4, pp. 1261-1332. https://doi.org/10.1215/21562261-2019-0062

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Dam, Thomas Norman ; Møller, Jacob Schach. / Spin-boson type models analyzed using symmetries. In: Kyoto Journal of Mathematics. 2020 ; Vol. 60, No. 4. pp. 1261-1332.

Bibtex

@article{1fff22e42c1e4a95afbbcf1a1b689e09,
title = "Spin-boson type models analyzed using symmetries",
abstract = "We analyze a family of models for a qubit interacting with a bosonic field. This family of models is very large and contains models where higher-order perturbations of field operators are added to the Hamiltonian. The Hamiltonian has a special symmetry, called spin-parity symmetry, which plays a central role in our analysis. Using this symmetry, we find the domain of self-adjointness and we decompose the Hamiltonian into two fiber operators each defined on Fock space. We then prove the Hunziker-van Winter-Zhislin (HVZ) theorem for the fiber operators, and we single out a particular fiber operator which has a ground state if and only if the full Hamiltonian has a ground state. From these results, we deduce a simple criterion for the existence of an excited state.",
author = "Dam, {Thomas Norman} and M{\o}ller, {Jacob Schach}",
note = "Publisher Copyright: {\textcopyright} 2020 by Kyoto University Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = dec,
doi = "10.1215/21562261-2019-0062",
language = "English",
volume = "60",
pages = "1261--1332",
journal = "Kyoto Journal of Mathematics",
issn = "2156-2261",
publisher = "Duke University Press",
number = "4",

}

RIS

TY - JOUR

T1 - Spin-boson type models analyzed using symmetries

AU - Dam, Thomas Norman

AU - Møller, Jacob Schach

N1 - Publisher Copyright: © 2020 by Kyoto University Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/12

Y1 - 2020/12

N2 - We analyze a family of models for a qubit interacting with a bosonic field. This family of models is very large and contains models where higher-order perturbations of field operators are added to the Hamiltonian. The Hamiltonian has a special symmetry, called spin-parity symmetry, which plays a central role in our analysis. Using this symmetry, we find the domain of self-adjointness and we decompose the Hamiltonian into two fiber operators each defined on Fock space. We then prove the Hunziker-van Winter-Zhislin (HVZ) theorem for the fiber operators, and we single out a particular fiber operator which has a ground state if and only if the full Hamiltonian has a ground state. From these results, we deduce a simple criterion for the existence of an excited state.

AB - We analyze a family of models for a qubit interacting with a bosonic field. This family of models is very large and contains models where higher-order perturbations of field operators are added to the Hamiltonian. The Hamiltonian has a special symmetry, called spin-parity symmetry, which plays a central role in our analysis. Using this symmetry, we find the domain of self-adjointness and we decompose the Hamiltonian into two fiber operators each defined on Fock space. We then prove the Hunziker-van Winter-Zhislin (HVZ) theorem for the fiber operators, and we single out a particular fiber operator which has a ground state if and only if the full Hamiltonian has a ground state. From these results, we deduce a simple criterion for the existence of an excited state.

UR - http://www.scopus.com/inward/record.url?scp=85097661104&partnerID=8YFLogxK

U2 - 10.1215/21562261-2019-0062

DO - 10.1215/21562261-2019-0062

M3 - Journal article

AN - SCOPUS:85097661104

VL - 60

SP - 1261

EP - 1332

JO - Kyoto Journal of Mathematics

JF - Kyoto Journal of Mathematics

SN - 2156-2261

IS - 4

ER -