Ground states of a general class of quantum field Hamiltonians

Asao Arai, Masao Hirokawa

Research output: Contribution to journalArticle

30 Citations (Scopus)

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 languageEnglish
Pages (from-to)1085-1135
Number of pages51
JournalReviews in Mathematical Physics
Volume12
Issue number8
DOIs
Publication statusPublished - Jan 1 2000

Fingerprint

Quantum Fields
Ground State
ground state
existence theorems
Weak Limit
Regularity Conditions
regularity
Mechanical Systems
Quantum Systems
Existence Theorem
Bosons
Infrared
bosons
Model
Sufficient Conditions
Class

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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

In: Reviews in Mathematical Physics, Vol. 12, No. 8, 01.01.2000, p. 1085-1135.

Research output: Contribution to journalArticle

@article{4c7ceb2a05fa44c1a98365681504c6df,
title = "Ground states of a general class of quantum field Hamiltonians",
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.",
author = "Asao Arai and Masao Hirokawa",
year = "2000",
month = "1",
day = "1",
doi = "10.1142/S0129055X00000393",
language = "English",
volume = "12",
pages = "1085--1135",
journal = "Reviews in Mathematical Physics",
issn = "0129-055X",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "8",

}

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 -