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This article is cited in 7 scientific papers (total in 7 papers)
Spectrum of the two-particle Schrödinger operator on a lattice
S. N. Lakaeva, A. M. Khalkhuzhaevb a A. Navoi Samarkand State University
b Institute of Study of Regional Problems, Uzbekistan Academy of Sciences, Samarkand Branch
Abstract:
We consider the family of two-particle discrete Schrödinger operators
$H(k)$ associated with the Hamiltonian of a system of two fermions on
a $\nu$-dimensional lattice $\mathbb Z^{\nu}$, $\nu\geq 1$, where
$k\in\mathbb T^{\nu}\equiv(-\pi,\pi]^{\nu}$ is a two-particle quasimomentum. We
prove that the operator $H(k)$, $k\in\mathbb T^{\nu}$, $k\ne0$, has an eigenvalue
to the left of the essential spectrum for any dimension $\nu=1,2,\dots$ if
the operator $H(0)$ has a virtual level ($\nu=1,2$) or an eigenvalue
($\nu\geq 3$) at the bottom of the essential spectrum (of the two-particle
continuum).
Keywords:
spectral properties, two-particle discrete Schrödinger operator, Birman–Schwinger principle, virtual level, eigenvalue.
Received: 20.12.2005 Revised: 24.07.2007
Citation:
S. N. Lakaev, A. M. Khalkhuzhaev, “Spectrum of the two-particle Schrödinger operator on a lattice”, TMF, 155:2 (2008), 287–300; Theoret. and Math. Phys., 155:2 (2008), 754–765
Linking options:
https://www.mathnet.ru/eng/tmf6211https://doi.org/10.4213/tmf6211 https://www.mathnet.ru/eng/tmf/v155/i2/p287
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Abstract page: | 540 | Full-text PDF : | 278 | References: | 95 | First page: | 4 |
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