This article is cited in 11 papers

On the Structure of the Essential Spectrum of a Model Many-Body Hamiltonian

T. H. Rasulov

A. Navoi Samarkand State University

Abstract: In this paper, we study the essential spectrum of a model lattice Hamiltonian describing a system with fluctuating number of particles ($0\le n\le2$) in the quasimomentum representation. The spectral properties are described in terms of the boundary values of a function of a complex variable, whose meaning is that of the kernel of the Schur complement
$$ H_{11}-z-H_{12}(H_{22}-z)^{-1}H_{12}^*. $$


Keywords: Schur complement, quasimomentum representation, many-body problem, fluctuating number of particles, essential spectrum.

UDC: 517.984

Received: 20.03.2006

DOI: 10.4213/mzm4337

 English version: Mathematical Notes, 2008, 83:1, 80–87

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