Why the quantitative condition fails to reveal quantum adiabaticity

Dafa Li Dept of mathematical sciences, Tsinghua University Man-Hong Yung Dept. of chemistry and chemical biology, Harvard University, USA

Theoretical Physics mathscidoc:1702.39002

New Journal of Physics, 16, 053023, 2014.5
The quantitative adiabatic condition (QAC), or quantitative condition, is a convenient (a priori) tool for estimating the adiabaticity of quantum evolutions. However, the range of the applicability of QAC is not well understood. It has been shown that QAC can become insufficient for guaranteeing the validity of the adiabatic approximation, but under what conditions the QAC would become necessary has become controversial. Furthermore, it is believed that the inability for the QAC to reveal quantum adiabaticity is due to induced resonant transitions. However, it is not clear how to quantify these transitions in general. Here we present a progress to this problem by finding an exact relation that can reveal how transition amplitudes are related to QAC directly. As a posteriori condition for quantum adiabaticity, our result is universally applicable to any (nondegenerate) quantum system and gives a clear picture on how QAC could become insufficient or unnecessary for the adiabatic approximation, which is a problem that has gained considerable interest in the literature in recent years
adiabatic computing, quantum adiabatic condition, adiabatic approximation
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  • the paper has been selected by the editors of New Journal of Physics for inclusion in the exclusive ‘Highlights of 2014’ collection. Papers are chosen on the basis of referee endorsement, novelty, scientific impact and broadness of appeal.
@inproceedings{dafa2014why,
  title={Why the quantitative condition fails to reveal quantum adiabaticity},
  author={Dafa Li, and Man-Hong Yung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170217232018528113465},
  booktitle={New Journal of Physics},
  volume={16},
  pages={053023},
  year={2014},
}
Dafa Li, and Man-Hong Yung. Why the quantitative condition fails to reveal quantum adiabaticity. 2014. Vol. 16. In New Journal of Physics. pp.053023. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170217232018528113465.
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