Discrete eigenvalues of the spin-boson Hamiltonian with two photons: on a problem of Minlos and Spohn

Abstract

Under minimal regularity conditions on the photon dispersion and the coupling function, we prove that the spin-boson model with two massless photons in ${\mathbb{R}}^d$ cannot have more than two bound state energies whenever the coupling strength is sufficiently strong.

Typos corrected, Lemma 2.1 of the previous version is removed due to a gap in its proof. The main result of the paper thus holds for sufficiently strong coupling

References in corpus (3)

• Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors
• Ergodicity of the Spin-Boson Model for arbitrary coupling strength
• Lower Spectral Branches of a Spin-Boson Model