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.
| Original language | English |
|---|---|
| Pages (from-to) | 455-503 |
| Number of pages | 49 |
| Journal | Journal of Functional Analysis |
| Volume | 151 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Dec 15 1997 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Analysis
Cite this
On the existence and uniqueness of ground states of a generalized spin-boson model. / Arai, Asao; Hirokawa, Masao.
In: Journal of Functional Analysis, Vol. 151, No. 2, 15.12.1997, p. 455-503.Research output: Contribution to journal › Article
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TY - JOUR
T1 - On the existence and uniqueness of ground states of a generalized spin-boson model
AU - Arai, Asao
AU - Hirokawa, Masao
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.
UR - http://www.scopus.com/inward/record.url?scp=0031574581&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0031574581&partnerID=8YFLogxK
U2 - 10.1006/jfan.1997.3140
DO - 10.1006/jfan.1997.3140
M3 - Article
AN - SCOPUS:0031574581
VL - 151
SP - 455
EP - 503
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -