We initiate the study of relaxation to quantum equilibrium over long timescales in pilot-wave theory. We simulate the time evolution of the coarse-grained H-function Hbar(t) for a two-dimensional harmonic oscillator. For a (periodic) wave function that is a superposition of the first 25 energy states we confirm an approximately exponential decay of Hbar over five periods. For a superposition of only the first four energy states we are able to calculate Hbar(t) over 50 periods. We find that the decay of Hbar saturates after about 20 periods, with a residue (exceeding 10% of the initial value) that shows no sign of decaying in the subsequent 30 periods. Possible cosmological implications are discussed.
Date added: Tue, 8 Oct 13