Geodesic
Asymptotics of the~discrete spectrum of a~model operator associated with a~system of three particles on a~lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 34-44

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We consider a model Schrödinger operator $H_\mu$ associated with a system of three particles on the three-dimensional lattice $\mathbb Z^3$ with a functional parameter of special form. We prove that if the corresponding Friedrichs model has a zero-energy resonance, then the operator $H_\mu$ has infinitely many negative eigenvalues accumulating at zero (the Efimov effect). We obtain the asymptotic expression for the number of eigenvalues of $H_\mu$ below $z$ as $z\to-0$.
Keywords: model operator, Friedrichs model, Birman–Schwinger principle, Efimov effect, Hilbert–Schmidt operator, zero-energy resonance, discrete spectrum. 
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     author = {T. H. Rasulov},
     title = {Asymptotics of the~discrete spectrum of a~model operator associated with a~system of three particles on a~lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {163},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a2/}
}
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T. H. Rasulov. Asymptotics of the~discrete spectrum of a~model operator associated with a~system of three particles on a~lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 34-44. http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a2/