Equilibration of Isolated Macroscopic Quantum Systems under Experimentally Realistic Conditions

TL;DR

This paper shows that isolated macroscopic quantum systems tend to reach a steady state after initial transients, under realistic conditions, with deviations becoming negligible or rare, supporting the idea of quantum equilibration.

Contribution

The paper provides a rigorous analysis demonstrating equilibration of macroscopic quantum systems under conditions that are experimentally realistic.

Findings

Deviations from steady state become unmeasurably small after initial transients.

Equilibration occurs under conditions like limited degeneracies and sufficient energy level population.

Experimental conditions typically satisfy prerequisites for quantum equilibration.

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.