On the existence and uniqueness of ground states of a generalized spin-boson model

Asao Arai; Masao Hirokawa

doi:10.1006/jfan.1997.3140

On the existence and uniqueness of ground states of a generalized spin-boson model

Asao Arai, Masao Hirokawa

Research output: Contribution to journal › Article › peer-review

91 Citations (Scopus)

Abstract

A generalization of the standard spin-boson model is considered. The HamiltonianH(α) of the model with a coupling parameterα∈Racts in the tensor product H⊕F_bof a Hilbert space H and the boson (symmetric) Fock space F_boverL²(R^ν). The existence and uniqueness of ground states ofH(α) are investigated. The degeneracy of the ground states is also discussed. The results obtained arenonperturbative. The methods used are those of constructive quantum field theory and the min-max principle. An exact asymptotic formula for the ground state energy ofH(α) as |α|→∞ is also established.

Original language	English
Pages (from-to)	455-503
Number of pages	49
Journal	Journal of Functional Analysis
Volume	151
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1997.3140
Publication status	Published - Dec 15 1997
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

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10.1006/jfan.1997.3140

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title = "On the existence and uniqueness of ground states of a generalized spin-boson model",

abstract = "A generalization of the standard spin-boson model is considered. The HamiltonianH(α) of the model with a coupling parameterα∈Racts in the tensor product H⊕Fbof a Hilbert space H and the boson (symmetric) Fock space FboverL2(Rν). The existence and uniqueness of ground states ofH(α) are investigated. The degeneracy of the ground states is also discussed. The results obtained arenonperturbative. The methods used are those of constructive quantum field theory and the min-max principle. An exact asymptotic formula for the ground state energy ofH(α) as |α|→∞ is also established.",

author = "Asao Arai and Masao Hirokawa",

note = "Funding Information: * Work supported by Grants-In-Aid 07640152 and 08454021 for science research from the Ministry of Education, Japan. -Part of work was done while M. H. was a researcher at the Advanced Research Laboratory, Hitachi Ltd.",

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T1 - On the existence and uniqueness of ground states of a generalized spin-boson model

AU - Arai, Asao

AU - Hirokawa, Masao

N1 - Funding Information: * Work supported by Grants-In-Aid 07640152 and 08454021 for science research from the Ministry of Education, Japan. -Part of work was done while M. H. was a researcher at the Advanced Research Laboratory, Hitachi Ltd.

PY - 1997/12/15

Y1 - 1997/12/15

N2 - A generalization of the standard spin-boson model is considered. The HamiltonianH(α) of the model with a coupling parameterα∈Racts in the tensor product H⊕Fbof a Hilbert space H and the boson (symmetric) Fock space FboverL2(Rν). The existence and uniqueness of ground states ofH(α) are investigated. The degeneracy of the ground states is also discussed. The results obtained arenonperturbative. The methods used are those of constructive quantum field theory and the min-max principle. An exact asymptotic formula for the ground state energy ofH(α) as |α|→∞ is also established.

AB - A generalization of the standard spin-boson model is considered. The HamiltonianH(α) of the model with a coupling parameterα∈Racts in the tensor product H⊕Fbof a Hilbert space H and the boson (symmetric) Fock space FboverL2(Rν). The existence and uniqueness of ground states ofH(α) are investigated. The degeneracy of the ground states is also discussed. The results obtained arenonperturbative. The methods used are those of constructive quantum field theory and the min-max principle. An exact asymptotic formula for the ground state energy ofH(α) as |α|→∞ is also established.

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On the existence and uniqueness of ground states of a generalized spin-boson model

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