Asymptotic estimates and borel resummation for a doubly anharmonic oscillator

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Abstract

The large-order behavior of perturbation theory for an oscillator with both quartic and sextic anharmonicity is examined. Two approaches are considered: an explicit double expansion in the two coupling constants and a single expansion in the number of loops. A two-variable extension of the Borel resummation technique is developed and applied to the double series, and the standard one-variable resummation technique is applied to the loop expansion. Numerical values for the ground-state energy are calculated in each case and the two procedures are compared.

Original languageEnglish (US)
Pages (from-to)3754-3767
Number of pages14
JournalPhysical Review D
Volume19
Issue number12
DOIs
StatePublished - Jan 1 1979

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