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arXiv:1104.0277 · Physical Review Letters

Comment on “Quantitative Condition is Necessary in Guaranteeing the Validity of the Adiabatic Approximation”

Meisheng Zhao, Jianda Wu

Published Apr 1, 2011• 13 citations
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Abstract

A Comment on the Letter by D. M. Tong, Phys. Rev. Lett. 104, 120401 (2010). Also, see Comment Phys. Rev. Lett. 106, 138902 (2011) by Daniel Comparat, on the same Letter by D. M. Tong, Phys. Rev. Lett. 104, 120401 (2010). The author of the Letter offers a Reply to both Comments.
DOI
10.1103/physrevlett.106.138901

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The quantum adiabatic theorem plays an important role in quantum mechanics. However, counter-examples were produced recently, indicating that their transition probabilities do not converge as predicted by the adiabatic theorem [K. P. Marzlin et al., Phys. Rev. Lett. 93, 160408 (2004); D. M. Tong et al., Phys. Rev. Lett. 95, 110407 (2005)]. For a special class of Hamiltonians, we examine the standard criterion for adiabatic evolution experimentally and theoretically, as well as three newly suggested adiabatic conditions. We show that the standard criterion is neither sufficient nor necessary.