Geodesic
Essential and Discrete Spectra of the Three-Particle Schr\"odinger Operator on a Lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 3, pp. 478-503

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We consider the system of three quantum particles (two are bosons and the third is arbitrary) interacting by attractive pair contact potentials on a three-dimensional lattice. The essential spectrum is described. The existence of the Efimov effect is proved in the case where either two or three two-particle subsystems of the three-particle system have virtual levels at the left edge of the three-particle essential spectrum for zero total quasimomentum ($K=0$). We also show that for small values of the total quasimomentum ($K\ne 0$), the number of bound states is finite.
Keywords: essential spectrum, virtual level, channel operator, discrete spectrum, Weyl inequality, Hilbert–Schmidt operator. 
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     author = {S. N. Lakaev and M. I. Muminov},
     title = {Essential and {Discrete} {Spectra} of the {Three-Particle} {Schr\"odinger} {Operator} on a {Lattice}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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S. N. Lakaev; M. I. Muminov. Essential and Discrete Spectra of the Three-Particle Schr\"odinger Operator on a Lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 3, pp. 478-503. http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a9/