Geodesic
Spectral properties of a two-particle Hamiltonian on a lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 3, pp. 482-496 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a system of two arbitrary quantum particles on a three-dimensional lattice with some dispersion functions (describing particle transport from a site to a neighboring site). The particles interact via an attractive potential at only the nearest-neighbor sites. We study how the number of eigenvalues of a family of 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. We find the conditions under which the operator $h(\mathbf 0)$ has a double or triple virtual level at zero depending on the particle interaction energy.
Keywords: two-particle Hamiltonian on a lattice, virtual level, virtual-level multiplicity, eigenvalue, positive operator. 
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M. I. Muminov; A. M. Hurramov. Spectral properties of a two-particle Hamiltonian on a lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 3, pp. 482-496. http://geodesic.mathdoc.fr/item/TMF_2013_177_3_a4/

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