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On the structure of the essential spectrum of a model many-body Hamiltonian

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Abstract

In this paper, we study the essential spectrum of a model lattice Hamiltonian describing a system with fluctuating number of particles (0 ≤ n ≤ 2) 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

$$ H_{11} - z - H_{12} \left( {H_{22} - z} \right)^{ - 1} H_{12}^ * . $$

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Authors and Affiliations

  1. A. Navoi Samarkand State University, Navoi Samrkand, Russia

    T. Kh. Rasulov

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  1. T. Kh. Rasulov
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Correspondence to T. Kh. Rasulov.

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Original Russian Text © T. Kh. Rasulov, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 1, pp. 86–94.

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Rasulov, T.K. On the structure of the essential spectrum of a model many-body Hamiltonian. Math Notes 83, 80–87 (2008). https://doi.org/10.1134/S0001434608010100

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