title: Quantitative conditions do not guarantee the validity of the adiabatic approximation.
abstract: In this Letter, we point out that the widely used quantitative conditions in the adiabatic theorem are insufficient in that they do not guarantee the validity of the adiabatic approximation. We also reexamine the inconsistency issue raised by Marzlin and Sanders [Phys. Rev. Lett. 93, 160408 (2004)] and elucidate the underlying cause.
authors.affiliation: Department of Physics, Shandong Normal University, Jinan 250014, Peoples Republic of China. phytdm@nus.edu.sg
authors.forename: D M
authors.initials: DM
authors.lastname: Tong
authors.forename: K
authors.initials: K
authors.lastname: Singh
authors.forename: L C
authors.initials: LC
authors.lastname: Kwek
authors.forename: C H
authors.initials: CH
authors.lastname: Oh