On the structure of the essential spectrum of the three-particle Schr\"{o}dinger operators on a lattice
Albeverio, Sergio ; Lakaev, Saidakhmat N. ; Muminov, Zakhriddin I.
arXiv, 0312050 / Harvested from arXiv
Text on arXiv
A system of three quantum particles on the three-dimensional lattice $\Z^3$ with arbitrary "dispersion functions" having non-compact support and interacting via short-range pair potentials is considered. The energy operators of the systems of the two-and three-particles on the lattice $\Z^3$ in the coordinate and momentum representations are described as bounded self-adjoint operators on the corresponding Hilbert spaces. For all sufficiently small nonzero values of the two-particle quasi-momentum $k\in (-\pi,\pi]^3$ the finiteness of the number of eigenvalues of the two-particle discrete Schr\"odinger operator $h_\alpha(k)$ below the continuous spectrum is established. A location of the essential spectrum of the three-particle discrete Schr\"odinger operator $H(K),K\in (-\pi,\pi]^3$ the three-particle quasi-momentum, by means of the spectrum of $h_\alpha(k)$ is described. It is established that the essential spectrum of $H(K), K\in (-\pi,\pi]^3$ consists of a finitely many bounded closed intervals.
Publié le : 2003-12-19
Classification:  Mathematical Physics,  Mathematics - Spectral Theory,  Primary: 81Q10, Secondary: 35P20, 47N50 
@article{0312050,
     author = {Albeverio, Sergio and Lakaev, Saidakhmat N. and Muminov, Zakhriddin I.},
     title = {On the structure of the essential spectrum of the three-particle
  Schr\"{o}dinger operators on a lattice},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0312050}
}

Albeverio, Sergio; Lakaev, Saidakhmat N.; Muminov, Zakhriddin I. On the structure of the essential spectrum of the three-particle
  Schr\"{o}dinger operators on a lattice. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0312050/