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arXiv · 0704.3445

Lower Spectral Branches of a Spin-Boson Model

Nicolae Angelescu·Robert Minlos·Jean Ruiz·Valentin Zagrebnov
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Abstract

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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Nicolae Angelescu, Robert Minlos, Jean Ruiz, Valentin Zagrebnov. 2008-10-28. Lower Spectral Branches of a Spin-Boson Model. https://doi.org/10.1063/1.2987721

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