Finite-time quantum equilibration for continuous variables

TL;DR

This paper extends quantum equilibration theory to infinite-dimensional systems with continuous spectra, providing a framework for finite-time equilibration estimates, which was previously limited to finite-dimensional systems.

Contribution

It develops a novel framework for quantum equilibration in infinite-dimensional systems with continuous spectra, extending previous finite-dimensional results.

Findings

Finite-time equilibration estimates are derived for systems with continuous spectra.

The framework generalizes existing finite-dimensional quantum equilibration results.

Constraints are necessary for finite-time equilibration in infinite-dimensional systems.

Abstract

Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the dynamics-generating Hamiltonians have continuous spectrum. The main goal of this paper will be to propose a framework to extend the results obtained by Short in, where estimates for the equilibration-on-average and effective equilibration for the case of Hamiltonians with continuous spectrum are derived. We will show that in the latter setting, it is compulsory to constrain ourselves to finite time equilibration; we then develop estimates analogous to the main results in the proposed setting.