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arXiv · 1204.2318

A note on the switching adiabatic theorem

Alexander Elgart·George A. Hagedorn
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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 $G^α$ 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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Alexander Elgart, George A. Hagedorn. 2012-07-07. A note on the switching adiabatic theorem. https://doi.org/10.1063/1.4748968

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