On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum Asymptotics

Author: Albeverio Sergio   Lakaev Saidakhmat   Rasulov Tulkin  

Publisher: Springer Publishing Company

ISSN: 0022-4715

Source: Journal of Statistical Physics, Vol.127, Iss.2, 2007-04, pp. : 191-220

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Abstract

A model operator H associated with the energy operator of a system describing three particles in interaction, without conservation of the number of particles, is considered. The location of the essential spectrum of H is described. The existence of infinitely many eigenvalues (resp. the finiteness of eigenvalues) below the bottom τess(H) of the essential spectrum of H is proved for the case where the associated Friedrichs model has a threshold energy resonance (resp. a threshold eigenvalue). For the number N(z) of eigenvalues of H lying below z < τess(H) the following asymptotics is found