Is the Adiabatic Approximation Inconsistent?

Solomon Duki; H. Mathur; Onuttom Narayan

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Is the Adiabatic Approximation Inconsistent?

Solomon Duki·H. Mathur·Onuttom Narayan

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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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Solomon Duki, H. Mathur, Onuttom Narayan. 2006-07-28. Is the Adiabatic Approximation Inconsistent?. https://arxiv.org/abs/quant-ph/0510131

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