The Threshold effects for the two-particle Hamiltonians on lattices
Albeverio, Sergio ; Lakaev, Saidakhmat N. ; Makarov, Konstantin A. ; Muminov, Zahriddin I.
arXiv, 0501013 / Harvested from arXiv
Text on arXiv
For a wide class of two-body energy operators $h(k)$ on the three-dimensional lattice $\bbZ^3$, $k$ being the two-particle quasi-momentum, we prove that if the following two assumptions (i) and (ii) are satisfied, then for all nontrivial values $k$, $k\ne 0$, the discrete spectrum of $h(k)$ below its threshold is non-empty. The assumptions are: (i) the two-particle Hamiltonian $h(0)$ corresponding to the zero value of the quasi-momentum has either an eigenvalue or a virtual level at the bottom of its essential spectrum and (ii) the one-particle free Hamiltonians in the coordinate representation generate positivity preserving semi-groups.
Publié le : 2005-01-06
Classification:  Mathematical Physics,  Mathematics - Spectral Theory,  Primary: 81Q10, Secondary: 35P20, 47N50 
@article{0501013,
     author = {Albeverio, Sergio and Lakaev, Saidakhmat N. and Makarov, Konstantin A. and Muminov, Zahriddin I.},
     title = {The Threshold effects for the two-particle Hamiltonians on lattices},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0501013}
}

Albeverio, Sergio; Lakaev, Saidakhmat N.; Makarov, Konstantin A.; Muminov, Zahriddin I. The Threshold effects for the two-particle Hamiltonians on lattices. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0501013/