Employing feedback in adiabatic quantum dynamics

We study quantum adiabatic dynamics, where the slowly moving field is influenced by system's state (feedback). The information for the feedback is gained from non-disturbating measurements done on an ensemble of identical non-interacting systems. The situation without feedback is governed by the adiabatic theorem: adiabatic energy level populations stay constant, while the adiabatic eigenvectors get a specific phase contribution (Berry phase). However, under feedback the adiabatic theorem does not hold: the adiabatic populations satisfy a closed equation of motion that coincides with the replicator dynamics well-known by its applications in evolutionary game theory. The feedback generates a new gauge-invariant adiabatic phase, which is free of the constraints on the Berry phase (e.g., the new phase is non-zero even for real adiabatic eigenfunctions).