On the Existence and Uniqueness of Ground States of a Generalized Spin-Boson Model

✍ Scribed by Asao Arai; Masao Hirokawa

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 607 KB
• Volume: 151
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1997.3140

✦ Synopsis

A generalization of the standard spin-boson model is considered. The Hamiltonian H(:) of the model with a coupling parameter : # R acts in the tensor product H F b of a Hilbert space H and the boson (symmetric) Fock space F b over L 2 (R & ). The existence and uniqueness of ground states of H(:) are investigated. The degeneracy of the ground states is also discussed. The results obtained are nonperturbative. The methods used are those of constructive quantum field theory and the min-max principle. An exact asymptotic formula for the ground state energy of H(:) as |:| Ä is also established. 1997 Academic Press Contents. 1. Introduction and main results. 2. Proof of Proposition 1.1. 3. Proof of Theorem 1.2. 3.1. A finite volume approximation. 3.2. Completion of proof of Theorem 1.2. 4. Proof of Theorem 1.3. 4.1. Some estimates on the ground states. 4.2. Completion of proof of Theorem 1.3. 5. Proof of Proposition 1.4. 6. Proof of Theorem 1.5. 7. Proof of Theorem 1.6.