Equilibration of quantum hard rods in one dimension

We study the out-of-equilibrium evolution of a strongly interacting quantum spin chain which is mapped on a system of hard rods that are coherently deposited on and removed from a lattice. We show that this closed quantum system approaches an equilibrium steady state which strongly resembles a microcanonical ensemble of classical hard rods. Starting from the fully coherent evolution equation we derive a master equation for the evolution of the number of hard rods on the lattice. This equation not only captures properties of the equilibrium state but also describes the dynamical non-equilibrium evolution into it for the majority of initial conditions. We analyze this in detail for hard rods of varying size.