Typical perturbation theory: Conditions, accuracy, and comparison with a mesoscopic case.

Abstract

The perturbation theory based on typicality introduced by Dabelow and Reimann [Phys. Rev. Lett. 124, 120602 (2020)0031-900710.1103/PhysRevLett.124.120602] and further refined by Dabelow et al. [Phys. Rev. Res. 2, 033210 (2020)2643-156410.1103/PhysRevResearch.2.033210; J. Stat. Mech. (2021) 0131061742-546810.1088/1742-5468/abd026] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while relying on only a few parameters. Even though the authors present various examples to demonstrate the effectiveness of the theory, the conditions used in its derivation are often not thoroughly checked. It is argued that this is justified (without analytical reasoning) by the robustness of the theory. In the paper at hand, said perturbation theory is tested on three spin-based models. The following criteria are taken into focus: the fulfillment of the conditions, the accuracy of the predicted dynamics, and the relevance of the results with respect to a mesoscopic case.