On the spectrum of an Hamiltonian in Fock space. Discrete spectrum Asymptotics

2005/08/14 by Sergio Albeverio, Albeverio, Sergio, Saidakhmat N. Lakaev +3
Mathematics · Physics and Astronomy · #47N50 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Primary: 81Q10 #Secondary: 35P20 #math-ph #math.FA #math.MP #msc:35P20 #msc:47N50 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.math-ph/0508028

arxiv created 2005/08/14 · arxiv updated 2009/12/01

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 precise location and structure of the essential spectrum of H is described. The existence of infinitely many eigenvalues below the bottom of the essential spectrum of H is proved for the case where an associated generalized Friedrichs model has a resonance at the bottom of its essential spectrum. An asymptotics for the number N(z) of eigenvalues below the bottom of the essential spectrum is also established. The finiteness of eigenvalues of H below the bottom of the essential spectrum is proved if the associated generalized Friedrichs model has an eigenvalue with energy at the bottom of its essential spectrum.

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