### Abstract

We consider a model of a quantum mechanical system coupled to a (massless) Bose field, called the generalized spin-boson model (A. Arai and M. Hirokawa, J. Funct. Anal. 151 (1997), 455-503), without infrared regularity condition. We define a regularized Hamiltonian H(ν) with a parameter ν ≥ 0 such that H = H(0) is the Hamiltonian of the original model. We clarify a relation between ground states of H(ν) and those of H by formulating sufficient conditions under which weak limits, as ν → 0, of the ground states of H(ν)'s are those of H. We also establish existence theorems on ground states of H(ν) and H under weaker conditions than in the previous paper mentioned above.

Original language | English |
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Pages (from-to) | 1085-1135 |

Number of pages | 51 |

Journal | Reviews in Mathematical Physics |

Volume | 12 |

Issue number | 8 |

DOIs | |

Publication status | Published - Jan 1 2000 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Reviews in Mathematical Physics*,

*12*(8), 1085-1135. https://doi.org/10.1142/S0129055X00000393

**Ground states of a general class of quantum field Hamiltonians.** / Arai, Asao; Hirokawa, Masao.

Research output: Contribution to journal › Article

*Reviews in Mathematical Physics*, vol. 12, no. 8, pp. 1085-1135. https://doi.org/10.1142/S0129055X00000393

}

TY - JOUR

T1 - Ground states of a general class of quantum field Hamiltonians

AU - Arai, Asao

AU - Hirokawa, Masao

PY - 2000/1/1

Y1 - 2000/1/1

N2 - We consider a model of a quantum mechanical system coupled to a (massless) Bose field, called the generalized spin-boson model (A. Arai and M. Hirokawa, J. Funct. Anal. 151 (1997), 455-503), without infrared regularity condition. We define a regularized Hamiltonian H(ν) with a parameter ν ≥ 0 such that H = H(0) is the Hamiltonian of the original model. We clarify a relation between ground states of H(ν) and those of H by formulating sufficient conditions under which weak limits, as ν → 0, of the ground states of H(ν)'s are those of H. We also establish existence theorems on ground states of H(ν) and H under weaker conditions than in the previous paper mentioned above.

AB - We consider a model of a quantum mechanical system coupled to a (massless) Bose field, called the generalized spin-boson model (A. Arai and M. Hirokawa, J. Funct. Anal. 151 (1997), 455-503), without infrared regularity condition. We define a regularized Hamiltonian H(ν) with a parameter ν ≥ 0 such that H = H(0) is the Hamiltonian of the original model. We clarify a relation between ground states of H(ν) and those of H by formulating sufficient conditions under which weak limits, as ν → 0, of the ground states of H(ν)'s are those of H. We also establish existence theorems on ground states of H(ν) and H under weaker conditions than in the previous paper mentioned above.

UR - http://www.scopus.com/inward/record.url?scp=0034374388&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034374388&partnerID=8YFLogxK

U2 - 10.1142/S0129055X00000393

DO - 10.1142/S0129055X00000393

M3 - Article

VL - 12

SP - 1085

EP - 1135

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 8

ER -