Generic evaluation of the relaxation time to equilibrium

TL;DR

This paper demonstrates that the relaxation time to equilibrium in macroscopic isolated quantum systems is largely independent of system size, depending at most polynomially, under specific conditions.

Contribution

It provides a generic estimation showing relaxation time's weak dependence on system size for non-integrable Hamiltonians with monotonic relaxation.

Findings

Relaxation time is almost independent of system size.

Relaxation time depends at most polynomially on system size.

Results hold for non-integrable Hamiltonians with monotonic relaxation.

Abstract

We evaluate the relaxation time to equilibrium, and especially show that it is almost independent from the system size for macroscopic isolated quantum systems. It at most polynomially depends on the system size. This estimation holds when the Hamiltonian is non-integrable, the initial deviation of the quantity of interest is of order its spectral norm, and the relaxation process is monotonic.