  Recently, Marzlin and Sanders (2004) demonstrated an inconsistency when the
adiabatic approximation was applied to specific, "inverse" time-evolving
systems. Following that, Tong et al. (2005) showed that the widely used
traditional adiabatic conditions are insufficient to guarantee the validity of
the adiabatic approximation for this class of systems. In this article we
explore the origin of these observations by a perturbative approach and find
that in first order approximation certain nonzero terms appear in the solution
which gives rise to the breakdown of the adiabatic approximation (despite the
fact that the traditional adiabatic conditions are satisfied). We argue that in
this case the Hamiltonian of Marzlin and Sanders' inverse time evolving system
cannot be written in terms of t/T, where T denotes the total evolution time. It
is further demonstrated that the new qualitative adiabatic condition of Ye et
al. (2005) performs well in some cases when the traditional conditions fail to
describe properly non-adiabatic evolution.
