The spectrum of a general three-particle lattice Hamiltonian
The author considers three interacting particles moving on a lattice \(\mathbb{Z}^\nu\). Under some assumptions for \(H_0\) and \(V\), it is shown that, for a sufficiently small \(\varepsilon\) and \(\nu\geq 3\), the Hamiltonian \(H(\varepsilon)= H_0+\varepsilon V\) is unitarily equivalent to the free Hamiltonian \(H_0\). This result is similar to the well-known Iorio-O'Carroll theorem for a system of interacting quantum particles moving in \(\mathbb{R}^\nu\) [\textit{M. Reed} and \textit{B. Simon}, Methods of modern mathematical physics, Vol. 3, Scattering theory (Academic Press, New York) (1979; Zbl 0405.47007); Vol. 4, Analysis of operators (Academic Press, New York) (1978; Zbl 0401.47001)].
scientific article; zbMATH DE number 999676