A note on the switching adiabatic theorem

  title={A note on the switching adiabatic theorem},
  author={A. Elgart and G. Hagedorn},
  journal={Journal of Mathematical Physics},
  • A. Elgart, G. Hagedorn
  • Published 2012
  • Physics, Mathematics
  • Journal of Mathematical Physics
  • 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. 
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