Invalidity of the quantitative adiabatic condition and general conditions for adiabatic approximations

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 sufficie...

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Bibliographic Details
Published in:Laser physics letters 2016-05, Vol.13 (5), p.55203
Main Author: Li, Dafa
Format: Article
Language:English
Subjects:
adiabatic approximation
adiabatic theorem
quantum adiabatic computing
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Summary: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.
ISSN:1612-2011
1612-202X
DOI:10.1088/1612-2011/13/5/055203