|
This article is cited in 38 scientific papers (total in 38 papers)
Essential and Discrete Spectra of the Three-Particle Schrödinger Operator on a Lattice
S. N. Lakaev, M. I. Muminov A. Navoi Samarkand State University
Abstract:
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.
Received: 23.07.2002
Citation:
S. N. Lakaev, M. I. Muminov, “Essential and Discrete Spectra of the Three-Particle Schrödinger Operator on a Lattice”, TMF, 135:3 (2003), 478–503; Theoret. and Math. Phys., 135:3 (2003), 849–871
Linking options:
https://www.mathnet.ru/eng/tmf197https://doi.org/10.4213/tmf197 https://www.mathnet.ru/eng/tmf/v135/i3/p478
|
Statistics & downloads: |
Abstract page: | 583 | Full-text PDF : | 254 | References: | 74 | First page: | 1 |
|