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The adiabatic theorem addresses the dynamics of a target instantaneouseigenstate of a time-dependent Hamiltonian. We use a Feshbach P-Q partitioningtechnique to derive a closed one-component integro-differential equation. Theresultant equation properly traces the footprint of the target eigenstate. Thephysical significance of the derived dynamical equation is illustrated by bothgeneral analysis and concrete examples. Surprisingly, we find an anomalousphenomenon showing that a dephasing white noise can enhance and even induceadiabaticity. This new phenomenon may naturally occur in many physical systems.We also show that white noises can also shorten the total duration of dynamicprocesses such as adiabatic quantum computing.

One Component Dynamical Equation and Noise Induced Adiabaticity