The number of eigenvalues for an Hamiltonian in Fock space

2005/01/12 by Sergio Albeverio, Saidakhmat N. Lakaev, Albeverio, Sergio +4
Mathematics · Physics and Astronomy · #47N50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 81Q10 #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Secondary: 35P20 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35P20 #msc:47N50 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.math-ph/0501037

23 pages

arxiv created 2005/01/12 · openalex publication_date 2005/01/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A model operator H corresponding to the energy operator of a system with non-conserved number n≤ 3 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 if the generalized Friedrichs model has a virtual level at the bottom of the essential spectrum and for the number N(z) of eigenvalues below z<0 an asymptotics established. The finiteness of eigenvalues of H below the bottom of the essential spectrum is proved if the generalized Friedrichs model has a zero eigenvalue at the bottom of its essential spectrum.

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