Positivity of the two-particle Hamiltonian on a lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 3, pp. 381-387
Voir la notice de l'article provenant de la source Math-Net.Ru
We consider a two-particle Hamiltonian on the $d$-dimensional lattice $\mathbb Z^d$.
We find a sufficient condition for the positivity of a family of operators
$h(k)$ appearing after the "separation of the center of mass" of a system of
two particles depending on the values of the total quasimomentum $k\in T^d$
(where $T^d$ is a $d$-dimensional torus). We use the obtained
result to show that the operator $h(k)$ has positive eigenvalues for nonzero
$k\in T^d$.
Keywords:
two-particle Hamiltonian on a lattice, virtual level, regular point, positive operator, discrete spectrum.
@article{TMF_2007_153_3_a4,
author = {M. I. Muminov},
title = {Positivity of the two-particle {Hamiltonian} on a lattice},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {381--387},
publisher = {mathdoc},
volume = {153},
number = {3},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_3_a4/}
}
M. I. Muminov. Positivity of the two-particle Hamiltonian on a lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 3, pp. 381-387. http://geodesic.mathdoc.fr/item/TMF_2007_153_3_a4/