Consistency of the Adiabatic Theorem

TL;DR

This paper reviews the quantum adiabatic approximation for both closed and open systems, critically examines claims of inconsistency, and clarifies the correct application to avoid misconceptions.

Contribution

It provides a comprehensive review of the adiabatic theorem's generalization to open systems and addresses recent claims of inconsistency with clarifications.

Findings

Clarifies the correct application of the adiabatic theorem

Addresses and refutes claims of inconsistency

Highlights importance of proper manipulation in proofs

Abstract

We review the quantum adiabatic approximation for closed systems, and its recently introduced generalization to open systems (M.S. Sarandy and D.A. Lidar, e-print quant-ph/0404147). We also critically examine a recent argument claiming that there is an inconsistency in the adiabatic theorem for closed quantum systems [K.P. Marzlin and B.C. Sanders, Phys. Rev. Lett. 93, 160408 (2004)] and point out how an incorrect manipulation of the adiabatic theorem may lead one to obtain such an inconsistent result.