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The essential spectrum of the three-particle discrete operator corresponding to a system of three fermions on a lattice

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Abstract

We consider a family of three-particle discrete Shrödinger operators H μ (K). These operators are associated with the Hamiltonian for a system of three identical particles (fermions) with pairwise two-particle interactions on neighboring junctions of the d-dimensional lattice Zd. We describe the location and the structure of the essential spectrum of the operator H μ (K) for all values of the three-particle quasi-momentum K ∈ Td and the interaction energy μ > 0.

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Authors and Affiliations

  1. Samarkand State University, Universiteskii bulv. 15, Samarkand, 140101, Republic of Uzbekistan

    A. M. Khalkhuzhaev

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  1. A. M. Khalkhuzhaev
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Correspondence to A. M. Khalkhuzhaev.

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Original Russian Text © A.M. Khalkhuzhaev, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 9, pp. 76–88.

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Khalkhuzhaev, A.M. The essential spectrum of the three-particle discrete operator corresponding to a system of three fermions on a lattice. Russ Math. 61, 67–78 (2017). https://doi.org/10.3103/S1066369X17090080

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  • DOI: https://doi.org/10.3103/S1066369X17090080

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