On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case
M. I. MuminovUniversiti Teknologi Malaysia 1 Faculty of Sciences, , 81310 Skudai, MalaysiaHagen NeidhardtWeierstrass Institute for Applied Analysis and Stochastics 2 , Mohrenstr. 39, D-10117 Berlin, GermanyTulkin H. RasulovBukhara State University 3 Faculty of Physics and Mathematics, , M. Ikbol str. 11, 200100 Bukhara, Uzbekistan
ABI
Abstract
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.
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