Spectral properties of a Hamiltonian of a four-particle system on a lattice
This paper deals with the Hamiltonian of a system of four arbitrary quantum particles with two-particle contact (noncompact) interaction potentials on a three-dimensional lattice perturbed by three-particle contact potentials. Particularly, it gives the location of the essential spectrum of the Schrödinger operator \(H(K)\) with respect to the values of the total quasi-momentum \(K \in [-\pi, \pi)^3\) corresponding to a four-particle system. After determination of possible sub-Hamiltonians of a four-particle system and decomposition of the sub-Hamiltonians into direct integral, the essential spectrum of the operator \(H(K)\) is described as the union of the spectra of the sub-Hamiltonians.
scientific article; zbMATH DE number 5975424