Variational Resummation of Divergent Series with known Large-Order Behavior

Abstract

Recently-developed variational perturbation expansions converge exponentially fast for positive coupling constants. They do not, however, possess the correct left-hand cut in the complex coupling constant plane, implying a wrong large-order behavior of their Taylor expansion coefficients. We correct this deficiency and present a method of resumming divergent series with their proper large-order behavior. For a given set of expansion coefficients, knowledge of the large-order behavior considerably improves the quality of the approximation.

Postscript, see also http://www.physik.fu-berlin.de/~kleinert/institution.html

References in corpus (6)

• Exact Five-Loop Renormalization Group Functions of ${\varphi }^4$-Theory with O(N)-Symmetric and Cubic Interactions. Critical Exponents up to $\ep^5$
• Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions
• Convergence behavior of variational perturbation expansion-- A method for locating Bender-Wu singularities
• 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

Cited by in corpus (5)

• Variational Interpolation Algorithm between Weak- and Strong-Coupling Expansions
• Smearing Formula for Higher-Order Effective Classical Potentials
• Resummation of anisotropic quartic oscillator. Crossover from anisotropic to isotropic large-order behavior
• A recursion technique for deriving renormalized perturbation expansions for one-dimensional anharmonic oscillator
• Observing Quantum Tunneling in Perturbation Series