  The adiabatic theorem addresses the dynamics of a target instantaneous
eigenstate of a time-dependent Hamiltonian. We use a Feshbach P-Q partitioning
technique to derive a closed one-component integro-differential equation. The
resultant equation properly traces the footprint of the target eigenstate. The
physical significance of the derived dynamical equation is illustrated by both
general analysis and concrete examples. Surprisingly, we find an anomalous
phenomenon showing that a dephasing white noise can enhance and even induce
adiabaticity. This new phenomenon may naturally occur in many physical systems.
We also show that white noises can also shorten the total duration of dynamic
processes such as adiabatic quantum computing.
