arXiv:1204.2318 · Journal of Mathematical Physics

A note on the switching adiabatic theorem

Alexander Elgart, George A. Hagedorn

Published Sep 18, 2012• 45 citations

Abstract

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.

DOI: 10.1063/1.4748968

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