Inconsistencies of the Adiabatic Theorem and the Berry Phase

Details Inconsistencies of the Adiabatic Theorem and the Berry Phase Inconsistencies of the Adiabatic Theorem and the Berry Phase

2004-05-21

arxiv.org/abs/quant-ph/0405129v2

Physics

Quantum Physics

Latex, 4 + pages, No figures, Resolution of the MS inconsistency given inquant-ph/0404022 and much more, This version now expa

Scientific paper

The adiabatic theorem states that if we prepare a quantum system in one of the instantaneous eigenstates then the quantum number is an adiabatic invariant and the state at a later time is equivalent to the instantaneous eigenstate at that time apart from phase factors. Recently, Marzlin and Sanders have pointed out that this could lead to apparent violation of unitarity. We resolve the Marzlin-Sanders inconsistency within the quantum adiabatic theorem. Yet, our resolution points to another inconsistency, namely, that the cyclic as well as non-cyclic adiabatic Berry phases may vanish under strict adiabatic condition. We resolve this inconsistency and develop an unitary operator decomposition method to argue for the validity of the adiabatic approximation.

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