1111.5195 (Juan Ortigoso)

Slight modification of the quantum adiabatic theorem    [PDF]

Juan Ortigoso

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. Although further analysis showed that the inconsistency arises from the existence of resonant terms in the Hamiltonian, recent work indicates that the debate about the full extent of the problem remains open. Here, by analyzing the standard proof of the theorem, we clarify its relation with the inconsistency, and obtain 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. Thus, the old consensus on the universal validity of both the adiabatic theorem and the adiabatic approximation, for slow systems with spectral gaps, should be reinstated.

View original: http://arxiv.org/abs/1111.5195