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
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Subject Classification: Primary: 81Q10, Secondary: 35P20, 47N50.
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Albeverio, S., Lakaev, S.N. & Rasulov, T.H. On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum Asymptotics. J Stat Phys 127, 191–220 (2007). https://doi.org/10.1007/s10955-006-9240-6
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DOI: https://doi.org/10.1007/s10955-006-9240-6