Multiplicity of virtual levels at the~lower edge of the~continuous spectrum of a~two-particle Hamiltonian on a~lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 3, pp. 329-341
Voir la notice de l'article provenant de la source Math-Net.Ru
We consider a system of two arbitrary quantum particles on a three-dimensional lattice with special dispersion functions (describing site-to-site particle transport), where the particles interact by a chosen attraction potential. We study how the number of eigenvalues of the family of the operators $h(k)$ depends on the particle interaction energy and the total quasimomentum $k\in\mathbb T^3$ (where $\mathbb T^3$ is a three-dimensional torus). Depending on the particle interaction energy, we obtain conditions under which the left edge of the continuous spectrum is simultaneously a multiple virtual level and an eigenvalue of the operator $h(\mathbf 0)$.
Keywords:
two-particle Hamiltonian on a lattice, virtual level, virtual level multiplicity, eigenvalue.
@article{TMF_2014_180_3_a3,
author = {M. I. Muminov and A. M. Hurramov},
title = {Multiplicity of virtual levels at the~lower edge of the~continuous spectrum of a~two-particle {Hamiltonian} on a~lattice},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {329--341},
publisher = {mathdoc},
volume = {180},
number = {3},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a3/}
}
TY - JOUR AU - M. I. Muminov AU - A. M. Hurramov TI - Multiplicity of virtual levels at the~lower edge of the~continuous spectrum of a~two-particle Hamiltonian on a~lattice JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2014 SP - 329 EP - 341 VL - 180 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a3/ LA - ru ID - TMF_2014_180_3_a3 ER -
%0 Journal Article %A M. I. Muminov %A A. M. Hurramov %T Multiplicity of virtual levels at the~lower edge of the~continuous spectrum of a~two-particle Hamiltonian on a~lattice %J Teoretičeskaâ i matematičeskaâ fizika %D 2014 %P 329-341 %V 180 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a3/ %G ru %F TMF_2014_180_3_a3
M. I. Muminov; A. M. Hurramov. Multiplicity of virtual levels at the~lower edge of the~continuous spectrum of a~two-particle Hamiltonian on a~lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 3, pp. 329-341. http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a3/