Convergence behavior of variational perturbation expansion-- A method for locating Bender-Wu singularities

Abstract

Variational perturbation expansions have recently been used to calculate directly the strong-coupling expansion coefficients of the anharmonic oscillator. The convergence is exponentially fast with superimposed oscillations, as recently observed empirically by the authors. In this note, the observed behavior is explained and used to determine accurately the magnitude and phase of the leading Bender-Wu singularity which is responsible for the finite convergence radius in the complex coupling constant plane.

Paper texfile convn.tex + figfiles in src (to appear in Phys. Lett. A 205, 101(1995)) Readable in hypertext format under http://www.physik.fu-berlin.de/~kleinert/kleiner_re234/preprint.html See also: http://www.physik.fu-berlin.de/~kleinert/institution.html

References in corpus (3)

• Variational Calculation of Effective Classical Potential at $T\ne 0$ to Higher Orders
• Precise variational tunneling rates for anharmonic oscillator with g<0
• Scaling property of variational perturbation expansion for general anharmonic oscillator

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