Equilibration of Isolated Macroscopic Quantum Systems under Experimentally Realistic Conditions

Abstract

In how far does an non-equilibrium initial ensemble evolve towards a stationary long time behavior for an isolated macroscopic quantum system? We demonstrate that deviations from a steady state indeed become unmeasurably small or exceedingly rare after initial transients have died out under the following conditions: The Hamilonian does not exhibit exceedingly large degeneracies of energy eigenvalues and energy gaps. A large number of energy levels is significantly populated by the initial ensemble. The system is observed by a measurement device with a reasonably bound working range compared to the resolution limit. The entire experiment, ending with the quantum mechanical measurement process, can only be repeated a "reasonable" number of times. It is argued that all these prerequisites for equilibration are fulfilled under many, if not all, experimentally realistic conditions.