The quantum adiabatic theorem in light of the Marzlin-Sanders inconsistency

Details The quantum adiabatic theorem in light of the Marzlin-Sanders inconsistency The quantum adiabatic theorem in light of the Marzlin-Sanders inconsistency

2011-11-22

arxiv.org/abs/1111.5195v3

Physics

Quantum Physics

Version submitted to Physical Review A. Title and abstract have been changed with respect to previous versions

Scientific paper

A new consensus that questions the perfunctory use of the quantum adiabatic theorem has emerged since Marzlin and Sanders [Phys. Rev. Lett. {\bf 93}, 160408 (2004)] showed the existence of an inconsistency in the applicability of the theorem. Further analysis proved that the inconsistency may arise from the existence of resonant terms in the Hamiltonian, but recent work indicates that the debate about the full extent of the problem remains open. Here, we show that key premises required in the standard demonstration of the theorem do not hold for the dual Hamiltonian involved in the Marzlin-Sanders inconsistency. Also, we found two simple conditions that allow us a rapid identification of systems for which the adiabatic approximation fails, in spite of satisfying traditional quantitave conditions that were believed to guarantee its validity.

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