Lower Spectral Branches of a Spin-Boson Model

Nicolae Angelescu (1) , Robert Minlos (2) , Jean Ruiz (3, 4) , Valentin Zagrebnov (3, 4)

1 NIPNE - National Institute of Physics and Nuclear Engineering
2 IITP - Institute for Information Transmission Problems
3 CPT - Centre de Physique Théorique - UMR 6207
4 CPT - Centre de Physique Théorique - UMR 7332

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.

Mots clés: Spin-boson model; two-level system; spectral branch

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Nicolae Angelescu, Robert Minlos, Jean Ruiz, Valentin Zagrebnov. Lower Spectral Branches of a Spin-Boson Model. 2007. ⟨hal-00143558v1⟩