Perturbative analysis of possible failures in the traditional adiabatic conditions

The breakdown of adiabatic approximation, demonstrated by Marzlin and Sanders [K.-P. Marzlin, B.C. Sanders, Phys. Rev. Lett. 93 (2004) 160408] and Tong et al. [D.M. Tong, et al., Phys. Rev. Lett. 95 (2005) 110407] for time-evolving “inverse” systems, is traced to the appearance of some nonzero terms in a perturbational treatment and is related to two time scales in the “inverse” systems' Hamiltonian. New adiabatic conditions of Ye et al. [M.-Y. Ye, et al., quant-ph/0509083] can restore the theoretical consistency.