Lower Spectral Branches of a Spin-Boson Model

Details Lower Spectral Branches of a Spin-Boson Model Lower Spectral Branches of a Spin-Boson Model

2007-04-25

arxiv.org/abs/0704.3445v2

Journal of Mathematical Physics 49 (2008) 102105

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1063/1.2987721

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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