On the essential spectrum of a model operator associated with the system of three particles on a lattice

Abstract


A model operator H associated with the system of three-identical particles on a lattice ℤ3 is considered. The location of the essential spectrum of H is described by the spectrum of the corresponding Friedrichs model, that is, the two-particle and three-particle branches of the essential spectrum of H are singled out. It is proved that the essential spectrum of H consists of no more than three bounded closed intervals. An appearance of two-particle branches on the both sides of the three-particle branch is shown. Moreover, we obtain an analogue of the Faddeev equation and its symmetric version, for the eigenfunctions of H.

About the authors

Tulkin Kh Rasulov

Bukhara State University, Physics and Mathematics Faculty

Email: rth@mail.ru
(к.ф.-м.н., доц.), доцент, каф. алгебры и анализа; Бухарский государственный университет; Bukhara State University, Physics and Mathematics Faculty

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