Quantum equilibration in finite time

TL;DR

This paper demonstrates that quantum systems equilibrate within finite time under realistic conditions, extending previous results by providing bounds on equilibration time and relaxing the non-degenerate energy gaps assumption.

Contribution

It proves finite-time equilibration bounds and relaxes the non-degenerate energy gaps condition in quantum systems.

Findings

Quantum subsystems equilibrate over finite times.

Equilibration occurs with less strict energy gap conditions.

Bounds on the time scale for quantum equilibration.

Abstract

It has recently been shown that small quantum subsystems generically equilibrate, in the sense that they spend most of the time close to a fixed equilibrium state. This relies on just two assumptions: that the state is spread over many different energies, and that the Hamiltonian has non-degenerate energy gaps. Given the same assumptions, it has also been shown that closed systems equilibrate with respect to realistic measurements. We extend these results in two important ways. First, we prove equilibration over a finite (rather than infinite) time-interval, allowing us to bound the equilibration time. Second, we weaken the non degenerate energy gaps condition, showing that equilibration occurs provided that no energy gap is hugely degenerate.