Sufficient Condition for Validity of Quantum Adiabatic Theorem

Zege Wu, Hang Zhou Yang

J. E. Avron, Alexander Elgart

Stefan Teufel

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

Vyacheslav I. Yukalov

Conditions for the validity of the quantum adiabatic approximation are analyzed. For the case of linear Hamiltonians, a simple and general sufficient condition is derived, which is valid for arbitrary spectra and any kind of time variation. It is shown that in some cases the found condition is necessary and sufficient. The adiabatic theorem is generalized for the case of nonlinear Hamiltonians.