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On The Number Of The Discrete Spectrum Of Two-Particle Discrete Schröodinger Operators, Zahriddin Muminov, Utkir Kuljanov, Shukhrat Alladustov
On The Number Of The Discrete Spectrum Of Two-Particle Discrete Schröodinger Operators, Zahriddin Muminov, Utkir Kuljanov, Shukhrat Alladustov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
We consider a family of discrete Schrö dinger operators hd(k), where k is the two-particle quasi-momentum varying in 𝕋d=(−π,π]d , associated to a system of two-particles on the d - dimensional lattice ℤd, d>1. The CwikelLieb-Rozenblum (CLR)-type estimates are written for hd(k) when the Fermi surface Ek-1(𝔢m(k)) of the associated dispersion relation is a one point set at em(k), the bottom of the essential spectrum. Moreover, when the Fermi surface Ek-1(𝔢m(k)) is of dimension d−1 or d−2, we …