标题： 自旋-玻色模型的低频谱分支 显示英文标题

标题： Lower Spectral Branches of a Spin-Boson Model

摘要： 我们研究了与玻色场弱耦合的两能级量子系统的谱结构（自旋-玻色模型）。 我们的分析允许避免玻色子数量的截断，如果它们的谱被一个正常数从下方限制。 我们证明，对于小的耦合常数，自旋-玻色哈密顿量的谱的下部包含（一个或两个）孤立本征值和（相应地，一个或两个）由玻色子动量$q$索引的原子$+ 1$-玻色子态流形。 后者的色散定律和广义本征函数被计算出来。 显示英文摘要

摘要： We study the structure of the spectrum of a two-level quantum system weakly coupled to a boson field (spin-boson model). Our analysis allows to avoid the cutoff in the number of bosons, if their spectrum is bounded below by a positive constant. We show that, for small coupling constant, the lower part of the spectrum of the spin-boson Hamiltonian contains (one or two) isolated eigenvalues and (respectively, one or two) manifolds of atom $+ 1$-boson states indexed by the boson momentum $q$. The dispersion laws and generalized eigenfunctions of the latter are calculated.