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Studies on the Generalized Spin-Boson Models

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Title: Studies on the Generalized Spin-Boson Models
Other Titles: 一般化されたスピン-ボソンモデルに関する研究
Authors: 寺西, 功哲1 Browse this author
Authors(alt): Teranishi, Noriaki1
Issue Date: 25-Mar-2014
Publisher: Hokkaido University
Abstract: We consider an abstract model which describes an interaction of non-relativistic particles with a Bose field. We show that the essential self-adjointness of the generalized spin-boson Hamiltonian with a quadratic boson interaction for all coupling constant and the Hamiltonian is self-adjoint if it is bounded from below under some conditions. We consider a unitary transformation of the Hamiltonian. Using the unitary transformation, we give a sufficient condition for the semiboundedness of the Hamiltonian.We are also interested in the ground states of the Hamiltonian. From the Birman-Schwinger principle, one can show that the Hamiltonian has no ground states for enough small coupling constants under a suitable condition. Finally, we apply our theorems to the Pauli-Fierz type Hamiltonian.
Conffering University: 北海道大学
Degree Report Number: 甲第11367号
Degree Level: 博士
Degree Discipline: 理学
Examination Committee Members: (主査) 教授 新井 朝雄, 教授 洞 彰人, 准教授 宮尾 忠宏
Degree Affiliation: 理学院(数学専攻)
Type: theses (doctoral)
Appears in Collections:学位論文 (Theses) > 博士 (理学)
課程博士 (Doctorate by way of Advanced Course) > 理学院(Graduate School of Science)

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