Validity of the quantum adiabatic theorem (5 pages)

Tao -, Yong

Jonas Larson, Stig Stenholm

Yong Tao

In this paper, we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem. The new sufficient condition can clearly remove the inconsistency and the counterexample of the quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 (2004) 160408].

V. S. Buslaev, E. A. Grinina

Zhaohui Wei, Mingsheng Ying

We show that in a quantum adiabatic evolution, even though the adiabatic approximation is valid, the total phase of the final state indicated by the adiabatic theorem may evidently differ from the actual total phase. This invalidates the application of the linearity and the adiabatic approximation simultaneously. Besides, based on this observation we point out the mistake in the traditional proof for the adiabatic theorem. This mistake is the root of the troubles that the adiabatic theorem has met. We also show that a similar mistake remains in some recent modifications of the traditional adiabatic theorem attempting to eliminate the troubles.

Pierre Lochak, Claude Meunier