Inconsistency and the adiabatic theorem

M. S. Sarandy, Lian-Ao Wu, Daniel A. Lidar

Yong Tao

In this paper, we note that there are two different types of inconsistencies of quantum adiabatic theorem in work of K. P. Marzlin and B. C. Sanders [Phys. Rev. Lett. 93, 160408, 2004], MS inconsistency and MS counterexample. Nevertheless, these two types are often confused as one by many authors. We shall point out that the inconsistencies of quantum adiabatic theorem raised by the relevant references just can be classified as these two types.

Rachel Berkowitz

Zhaoyan Wu, Li Zheng, Hui Yang

It is shown where the proof of "inconsistency in the application of the adiabatic theorem" goes wrong.

Mirjana Božić, R.J. Lombard, Z. Marić

Arun Kumar Pati, A. K. Rajagopal

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.