Tunnelling amplitudes from perturbation expansions

Variational perturbation theory for summing divergent tunnelling amplitudes

We present a method for evaluating divergent series with factorially growing coefficients of equal sign. The method is based on an analytic continuation of variational perturbation theory from the regime of alternating signs. We demonstrate its power first by applying it to the exactly known partition function of the anharmonic oscillator in zero space–time dimensions (the simple integral). The...

Perturbation of eigenfunction expansions.

Freezing in a Finite Slab Using Extensive Perturbation Expansions Method

In this paper Mathematica is used to solve the moving boundary problem of freezing in a finite slab for higher order perturbations. Mathematica is a new system which makes it possible to do algebra with computer. More specifically, it enables researchers to find the location of the ice at any time for as high order of perturbation as one whishes. Using of Mathematica and outer solution and an i...

Perturbation Expansions in Polynomial Root TrackingJ

In this short communication we suggest an alternative for root tracking algorithms that compute the roots explicitly. The proposed method is based on rst using any preferred algorithm to track the transversal model parameters and the subsequent use of the second order perturbation expansion for the associated companion matrix to approximate a single root of interest. The tracking of a single ro...

Convergence Behavior of Variational Perturbation Expansions

Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of strong-coupling expansions. For the anharmonic oscillator we explain the physical origin of the empirically observed convergence behavior which is exponentially fast with superimposed oscillations.