A note on the switching adiabatic theorem

Alexander Elgart, George A. Hagedorn

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21 Scopus 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.

Original languageEnglish
Article number102202
JournalJournal of Mathematical Physics
Volume53
Issue number10
DOIs
StatePublished - 12 Sep 2012
Externally publishedYes

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