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Is the Adiabatic Approximation Inconsistent?

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arxiv quant-ph/0510131 v2 pith:CP5VQTN3 submitted 2005-10-17 quant-ph

Solomon Duki , H.Mathur , Onuttom Narayan This is my paper
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keywords adiabaticapproximationconditionsevenevolutionhamiltonianinconsistentmarzlin
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abstract

Marzlin and Sanders \cite{marzlin} have shown rigorously that the adiabatic approximation can be very inaccurate when applied to a Hamiltonian $H(t)$ that generates the evolution $U^{\dagger} (t)$ even if it gives an excellent approximation to the evolution $U(t)$ generated by a dual Hamiltonian $h(t)$. We show that this is not inconsistent with the adiabatic theorem and find that in general even if $h(t)$ satisfies the conditions of the adiabatic theorem, $H(t)$ will likely violate those conditions.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Geometric Floquet Condition for Quantum Adiabaticity

    quant-ph 2023-02 unverdicted novelty 6.0 of 10

    Derives a stroboscopic geometric sufficient condition for adiabaticity in closed finite-dimensional periodically driven quantum systems from single-cycle Floquet data.

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