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Science China Physics Mechanics and Astronomy

Quantitative sufficient conditions for adiabatic approximation

HuaiXin Cao, Zhihua Guo, ZhengLi Chen, WenHu Wang

Published May 23, 2013• 24 citations
Publisher
DOI
10.1007/s11433-013-5127-0

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Abstract The adiabatic theorem was proposed about 90 years ago and has played an important role in quantum physics. The quantitative adiabatic condition constructed from eigenstates and eigenvalues of a Hamiltonian is a traditional tool to estimate adiabaticity and has proven to be the necessary and sufficient condition for adiabaticity. However, recently the condition has become a controversial subject. In this paper, we list some expressions to estimate the validity of the adiabatic approximation. We show that the quantitative adiabatic condition is invalid for the adiabatic approximation via the Euclidean distance between the adiabatic state and the evolution state. Furthermore, we deduce general necessary and sufficient conditions for the validity of the adiabatic approximation by different definitions.