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Asymptotic response of observables from divergent weak-coupling expansions: A fractional-calculus-assisted Padé technique
S DHATT, K BHATTACHARYYA
Published in -
2012
Volume: 86
   
Issue: 2
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. © 2012 American Physical Society.
About the journal
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Publisher-
ISSN1539-3755