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

Sergio Albeverio·Saidakhmat N. Lakaev·Tulkin H. Rasulov
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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 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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Sergio Albeverio, Saidakhmat N. Lakaev, Tulkin H. Rasulov. 2005-08-14. On the spectrum of an Hamiltonian in Fock space. Discrete spectrum Asymptotics. https://arxiv.org/abs/math-ph/0508028

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