Essential spectrum and spectral bounds of a three-particle Hamiltonian on a one-dimensional lattice

In this paper, we consider a model Hamiltonian describing a quantum-mechanical three-particle system on a one-dimensional lattice. The role of the two-particle discrete Schrödinger operator is played by a family of Friedrichs models. We investigate the case in which the kinetic part of the model Hamiltonian has a special structure. Two channel operators are constructed, and their spectra are determined using the spectral properties of the corresponding family of Friedrichs models. It is shown that the essential spectrum of the model Hamiltonian is given by the union of the spectra of the channel operators and consists of at most three intervals. Furthermore, estimates for the lower and upper bounds of these intervals are obtained.

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