Relaxation to equilibrium of expectation values in macroscopic quantum systems

A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally perturbed during a finite time, and then isolated for a sufficiently long time. We show a quantitative explanation that the initial microcanonical state typically reaches to a state whose expectation values are well-approximated by the average over another microcanonical ensemble.