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

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

2005-08-14

arxiv.org/abs/math-ph/0508029v2

Physics

Mathematical Physics

14 pages

Scientific paper

A model operator $H$ associated to a system of three-particles on the three dimensional lattice $\Z^3$ 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 $h_{\mu_\alpha}(0),\alpha=1,2,$ 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 $h_{\mu_\alpha}(0), \alpha=1,2,$ has a threshold eigenvalue.

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