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Asymptotic response of observables from divergent weak-coupling expansions: a fractional-calculus-assisted Padé
Sharmistha Dhatt1, Kamal Bhattacharyya
1Department of Chemistry, University of Calcutta, Kolkata, India. pcsdhatt@gmail.com
Abstract:
Appropriate constructions of Padé approximants are believed to provide reasonable estimates of the asymptotic (large-coupling) amplitude and exponent of an observable, given its weak-coupling expansion to some desired order. In many instances, however, sequences of such approximants are seen to converge very poorly. We outline here a strategy that exploits the idea of fractional calculus to considerably improve the convergence behavior. Pilot calculations on the ground-state perturbative energy series of quartic, sextic, and octic anharmonic oscillators reveal clearly the worth of our endeavor.
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