(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Muminov, Mukhiddin; Neidhardt, Hagen; Rasulov, Tulkin
A lattice model of radiative decay (so-called spin-boson model) of a
two level atom and at most two photons is considered. The location of the
essential spectrum is described. For any coupling constant the finiteness of
the number of eigenvalues below the bottom of its essential spectrum is
proved. The results are obtained by considering a more general model H for
which the lower bound of its essential spectrum is estimated. Conditions
which guarantee the finiteness of the number of eigenvalues of H below the
bottom of its essential spectrum are found. It is shown that the discrete
spectrum might be infinite if the parameter functions are chosen in a special
form.
