On the structure of the essential spectrum of the three-particle Schrödinger operators on a lattice

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dc.creatorAlbeverio, Sergio
dc.creatorLakaev, Saidakhmat N.
dc.creatorMuminov, Zakhriddin I.
dc.date2003-12-19
dc.date.accessioned2026-07-07T04:30:49Z
dc.date.available2026-07-07T04:30:49Z
dc.descriptionA system of three quantum particles on the three-dimensional lattice $\Z^3$ with arbitrary "dispersion functions" having non-compact support and interacting via short-range pair potentials is considered. The energy operators of the systems of the two-and three-particles on the lattice $\Z^3$ in the coordinate and momentum representations are described as bounded self-adjoint operators on the corresponding Hilbert spaces. For all sufficiently small nonzero values of the two-particle quasi-momentum $k\in (-π,π]^3$ the finiteness of the number of eigenvalues of the two-particle discrete Schrödinger operator $h_α(k)$ below the continuous spectrum is established. A location of the essential spectrum of the three-particle discrete Schrödinger operator $H(K),K\in (-π,π]^3$ the three-particle quasi-momentum, by means of the spectrum of $h_α(k)$ is described. It is established that the essential spectrum of $H(K), K\in (-π,π]^3$ consists of a finitely many bounded closed intervals.
dc.identifierhttps://arxiv.org/abs/math-ph/0312050
dc.identifierhttp://arxiv.org/abs/math-ph/0312050
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57602
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subjectPrimary: 81Q10, Secondary: 35P20, 47N50
dc.titleOn the structure of the essential spectrum of the three-particle Schrödinger operators on a lattice
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