On the number of eigenvalues of a model operator associated to a system of three-particles on lattices

2005/08/14 by Sergio Albeverio, Albeverio, Sergio, S. N. Lakaev +5
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #Numerical methods in inverse problems #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/0508029

14 pages

arxiv created 2006/08/14 · arxiv updated 2009/12/01

Abstract

A model operator H associated to a system of three-particles on the three dimensional lattice \Z³ and interacting via pair non-local potentials is studied. The following results are proven: (i) the operator H has infinitely many eigenvalues lying below the bottom of the essential spectrum and accumulating at this point, in the case, where both Friedrichs model operators h_μα(0),α=1,2, have threshold resonances. (ii) the operator H has a finite number of eigenvalues lying outside of the essential spectrum, in the case, where at least one of h_μα(0), α=1,2, has a threshold eigenvalue.

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