Employing feedback in adiabatic quantum dynamicsA. E. Allahverdyan1 and G. Mahler2
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
received 24 July 2008; accepted in final form 10 October 2008; published November 2008
published online 12 November 2008
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.
03.65.-w - Quantum mechanics.
03.65.Vf - Phases: geometric; dynamic or topological.
05.30.Ch - Quantum ensemble theory.
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