On the behavior of Padé approximants in the vicinity of avoided crossings

When linear Padé summation is applied to eigenvalue perturbation expansions near regions of parameter space where those eigenvalues undergo an avoided crossing, the Padé approximants may yield levels which cross diabatically, rather than displaying the proper avoided behavior. The purpose of this st...

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Bibliographic Details
Published in:The Journal of chemical physics 1996-06, Vol.104 (24), p.9870-9875
Main Authors: Dunn, Martin, Watson, Deborah K., Walkup, John R., Germann, Timothy C.
Format: Article
Language:English
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Summary:When linear Padé summation is applied to eigenvalue perturbation expansions near regions of parameter space where those eigenvalues undergo an avoided crossing, the Padé approximants may yield levels which cross diabatically, rather than displaying the proper avoided behavior. The purpose of this study is to elucidate the reasons for the peculiar behavior of Padé approximants in such situations. In particular, we demonstrate that the diabatic crossing is a natural consequence of using the (single-valued) Padé rational approximant to successfully resum series expansions of the multivalued energy function over much of the parameter space. This is illustrated with a perturbative treatment of the Barbanis Hamiltonian.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.471751