The semiclassical limit of the spin boson model

Abstract

The authors study the semiclassical limit of the spin boson model, where the spin remains quantized and the field is expanded around the classical limit of a large number of photons, using a phase representation due to Bialynicki-Birula and Bialynicki-Birula (1976). They derive the semiclassical Hamiltonian and prove that in the semiclassical expansion there always arises a back reaction of the atom on the field. The nearest-neighbour spacing distribution of levels is studied in the same limit and shown to be, in general, qualitatively different from the distribution for the original model. However, the comparison between the Dyson-Mehta statistics is also studied and no qualitative difference is visible for the function Delta 3.