Sufficiency Criterion for the Validity of the Adiabatic Approximation

Details Sufficiency Criterion for the Validity of the Adiabatic Approximation Sufficiency Criterion for the Validity of the Adiabatic Approximation

2007-04-10

arxiv.org/abs/0704.1184v1

Physical Review Letters 98, 150402, 2007

Physics

Quantum Physics

9 pages, no figure,appearing in PRL98(2007)150402

Scientific paper

We examine the quantitative condition which has been widely used as a criterion for the adiabatic approximation but was recently found insufficient. Our results indicate that the usual quantitative condition is sufficient for a special class of quantum mechanical systems. For general systems, it may not be sufficient, but it along with additional conditions is sufficient. The usual quantitative condition and the additional conditions constitute a general criterion for the validity of the adiabatic approximation, which is applicable to all $N-$dimensional quantum systems. Moreover, we illustrate the use of the general quantitative criterion in some physical models.

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