**One component quantum mechanics and target state tracing** - Lianao Wu

We use a Feshbach P-Q partitioning technique to derive a closed one-
component integro-differential equation for all linear system. The
resultant equation properly traces the footprint of the target state.
The
physical significance of the derived dynamical equation is illustrated by
both general analysis and concrete examples. We show that tracing a
target statel can be done by fast-changing external fields, even fast
noises. We illustrate
the results by quantum memory and controlled adiabatic paths.