• DOI:10.1063/1.4748968
Corpus ID: 62833788

A note on the switching adiabatic theorem

@article{Elgart2012ANO,
  title={A note on the switching adiabatic theorem},
  author={A. Elgart and G. Hagedorn},
  journal={Journal of Mathematical Physics},
  year={2012},
  volume={53},
  pages={102202}
}

A. Elgart, G. Hagedorn

Published 2012

Physics, Mathematics

Journal of Mathematical Physics

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We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class Gα as a function of time, and we show that the error in adiabatic approximation remains small for running times of order g−2 |ln g |6α. Here g denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian.