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

Asao Arai, Masao Hirokawa

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85 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⊕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 languageEnglish
Pages (from-to)455-503
Number of pages49
JournalJournal of Functional Analysis
Volume151
Issue number2
DOIs
Publication statusPublished - Dec 15 1997

All Science Journal Classification (ASJC) codes

  • Analysis

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