On the finiteness of the discrete spectrum of a \(3\times 3\) operator matrix
The author considers an operator matrix \(H\) associated with the lattice system describing three particles in interaction without conservation of the number of particles; this is a lattice analog of the spin-boson Hamiltonian (see [\textit{R. Minlos} and \textit{H. Spohn}, in: Topics in statistical and theoretical physics. F. A. Berezin memorial volume. Transl. ed. by A. B. Sossinsky. Providence, RI: American Mathematical Society. 159--193 (1996; Zbl 0881.47049)]. The main results deal with the structure of the essential and point spectra of \(H\). In particular, the author finds conditions guaranteeing the finiteness of the number of discrete eigenvalues located below the bottom of the three-particle branch of the essential spectrum.
scientific article; zbMATH DE number 6630282