### 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 - Aug 2000 |

Externally published | Yes |

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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