One- and Two-Particle Bound States in the Landau–Khalatnikov Bose-Liquid Model

We consider the Landau–Khalatnikov Hamiltonian of a quantum liquid restricted to the subspace of one- and two-particle states. We give a complete description of the spectrum of this Hamiltonian for any given value of the total momentum. In particular, we describe the bound state of two rotons, so-called biroton. These results about bound states are not based on any ad hoc hypotheses about roton-roton interaction. The conditions imposed on the quasi-particle dispersion law and on the qubic interaction term are rather general.