One-component dynamical equation and noise-induced adiabaticity

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. We find an interesting phenomenon showing that a dephasing white noise can enhance and even induce adiabaticity. This phenomenon, distinguishing itself from any artificial control process, may occur in natural physical processes. We also show that particular white noises can shorten the total duration of dynamic processing, such as in adiabatic quantum computing.