On the spectrum of an operator in truncated Fock space

Abstract

We study the spectrum of an operator matrix arising in the spectral analysis of the energy operator of the spin-boson model of radioactive decay with two bosons on the torus. An analytic description of the essential spectrum is established. Further, a criterion for the finiteness of the number of eigenvalues below the bottom of the essential spectrum is derived.

arXiv commentIn this version a number of typos have been corrected. 14 pages