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

TL;DR

This paper evaluates a perturbation theory based on typicality across three spin models, examining its conditions, accuracy, and relevance to mesoscopic systems, and highlights its robustness and applicability.

Contribution

It provides a thorough testing of the typicality-based perturbation theory on spin models, emphasizing the importance of condition fulfillment and accuracy in mesoscopic contexts.

Findings

The theory's conditions are generally satisfied in tested models.

Predicted dynamics closely match numerical results.

The approach is relevant for mesoscopic system analysis.

Abstract

The perturbation theory based on typicality introduced in Ref. [1] and further refined in Refs. [2, 3] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while relying only on 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.