Dynamics of thermalisation in small Hubbard-model systems

We study numerically the thermalisation and temporal evolution of the reduced density matrix for a two-site subsystem of a fermionic Hubbard model prepared far from equilibrium at a definite energy. Even for very small systems near quantum degeneracy, the subsystem can reach a steady state resembling equilibrium. This occurs for a non-perturbative coupling between the subsystem and the rest of the lattice where relaxation to equilibrium is Gaussian in time, in sharp contrast to perturbative results. We find similar results for random couplings, suggesting such behaviour is generic for small systems.