Employing feedback in adiabatic quantum dynamics

¹  Yerevan Physics Institute - Alikhanian Brothers Street 2, Yerevan 375036, Armenia
²  Institute of Theoretical Physics I, University of Stuttgart - Pfaffenwaldring 57, 70550 Stuttgart, Germany, EU

Corresponding author: aarmen@yerphi.am

Received: 24 July 2008
Accepted: 10 October 2008

Abstract

We study quantum adiabatic dynamics, where the slowly moving field is influenced by the system's state (feedback). The feedback is achieved either via mean-field quantum-classical interaction, or, alternatively, via non-disturbing 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 known by its numerous 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). In a particular case the adiabatic theorem can still hold, but the new phases are non-trivial.