Review of inconsistency of quantum adiabatic theorem

TL;DR

This paper clarifies the two distinct types of inconsistencies in the quantum adiabatic theorem identified in prior work, emphasizing the importance of correct classification to avoid confusion.

Contribution

It distinguishes and clarifies the two different inconsistency types in the quantum adiabatic theorem, which are often conflated in the literature.

Findings

Identification of two distinct inconsistency types

Clarification of common misconceptions

Improved understanding of quantum adiabatic theorem issues

Abstract

In this paper, we note that there are two different types of inconsistencies of quantum adiabatic theorem in work of K. P. Marzlin and B. C. Sanders [Phys. Rev. Lett. 93, 160408, 2004], MS inconsistency and MS counterexample. Nevertheless, these two types are often confused as one by many authors. We shall point out that the inconsistencies of quantum adiabatic theorem raised by the relevant references just can be classified as these two types.