Convergence to a stationary state for one-dimensional lattice quantum models of hard rods

A theorem on convergence to the limit during time evolution of the state of an infinite one-dimensional lattice quantum system is proved for the model of the motion of ideal hard rods. We consider one-dimensional lattice Fermi systems and boson systems. We give examples of states for which the conditions of the main theorems on convergence to a stationary state are satisfied.