Geodesic
Existence and analyticity of eigenvalues of a two-channel molecular resonance model
Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 3, pp. 341-351 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a family of operators $H_{\gamma\mu}(k)$, $k\in\mathbb T^d:= (-\pi,\pi]^d$, associated with the Hamiltonian of a system consisting of at most two particles on a $d$-dimensional lattice $\mathbb Z^d$, interacting via both a pair contact potential $(\mu>0)$ and creation and annihilation operators $(\gamma>0)$. We prove the existence of a unique eigenvalue of $H_{\gamma\mu}(k)$, $k\in\mathbb T^d$, or its absence depending on both the interaction parameters $\gamma,\mu\ge0$ and the system quasimomentum $k\in\mathbb T^d$. We show that the corresponding eigenvector is analytic. We establish that the eigenvalue and eigenvector are analytic functions of the quasimomentum $k\in\mathbb T^d$ in the existence domain $G\subset\mathbb T^d$.
Keywords: Hamiltonian, creation operator, eigenvalue, bound state, lattice. 
@article{TMF_2011_169_3_a1,
     author = {S. N. Lakaev and Sh. M. Latipov},
     title = {Existence and analyticity of eigenvalues of a~two-channel molecular resonance model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {341--351},
     year = {2011},
     volume = {169},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_169_3_a1/}
}
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S. N. Lakaev; Sh. M. Latipov. Existence and analyticity of eigenvalues of a two-channel molecular resonance model. Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 3, pp. 341-351. http://geodesic.mathdoc.fr/item/TMF_2011_169_3_a1/

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