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Abstract: The operator fidelity is a measure of the information-theoreticdistinguishability between perturbed and unperturbed evolutions. The responseof this measure to the perturbation may be formulated in terms of the operatorfidelity susceptibility OFS, a quantity which has been used to investigatethe parameter spaces of quantum systems in order to discriminate their regularand chaotic regimes. In this work we numerically study the OFS for a pair ofnon-linearly coupled two-dimensional harmonic oscillators, a model which isequivalent to that of a hydrogen atom in a uniform external magnetic field. Weshow how the two terms of the OFS, being linked to the main properties thatdifferentiate regular from chaotic behavior, allow for the detection of thismodel-s transition between the two regimes. In addition, we find that theparameter interval where perturbation theory applies is delimited from above bya local minimum of one of the analyzed terms.



Author: N. Tobias Jacobson, Paolo Giorda, Paolo Zanardi

Source: https://arxiv.org/







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