自旋玻色子模型的下谱支
Lower Spectral Branches of a Spin-Boson Model
摘要：
研究了与玻色子场弱耦合的二能级量子系统（自旋玻色子模型）的光谱结构。我们的分析可以避免截断玻色子的数量，如果他们的频谱是由一个正常数以下的限制。我们表明，对于较小的耦合常数，自旋玻色子Hamilton谱的下部包含（一个或两个）孤立的本征值和（分别，一个或两个）原子流形$+ 1$ -由玻色子动量$q$索引的玻色子态。计算了后者的色散律和广义本征函数。
英文摘要：
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.
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