Is the Adiabatic Approximation Inconsistent?

Details Is the Adiabatic Approximation Inconsistent? Is the Adiabatic Approximation Inconsistent?

2005-10-17

arxiv.org/abs/quant-ph/0510131v2

Physics

Quantum Physics

Expanded discussion of connection between Refs.[7] and [8] included

Scientific paper

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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