Automatic Loop Calculations with FeynArts, FormCalc, and LoopTools

This article describes three Mathematica packages for the automatic calculation of one-loop Feynman diagrams: the diagrams are generated with FeynArts, algebraically simplified with FormCalc, and finally evaluated numerically using the LoopTools package. The calculations are performed analytically as far as possible, with results given in a form well suited for numerical evaluation. The latter is straightforward with the utility programs provided by FormCalc (e.g. for translation into Fortran code) and the implementations of the one-loop integrals in LoopTools. The programs are also equipped for calculations in supersymmetric models.Comment: 6 pages, uses axodraw and npb.sty. Talk given at Loops and Legs 2000, Bastei, Germany, April 9-1

Efficient computation of the second-Born self-energy using tensor-contraction operations

In the nonequilibrium Green's function approach, the approximation of the correlation self-energy at the second-Born level is of particular interest, since it allows for a maximal speed-up in computational scaling when used together with the Generalized Kadanoff-Baym Ansatz for the Green's function. The present day numerical time-propagation algorithms for the Green's function are able to tackle first principles simulations of atoms and molecules, but they are limited to relatively small systems due to unfavourable scaling of self-energy diagrams with respect to the basis size. We propose an efficient computation of the self-energy diagrams by using tensor-contraction operations to transform the internal summations into functions of external low-level linear algebra libraries. We discuss the achieved computational speed-up in transient electron dynamics in selected molecular systems.Comment: 9 pages, 4 figures, 1 tabl

Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) hfbtho (v3.00): a new version of the program

We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck (iv) the regularization of zero-range pairing forces (v) the calculation of localization functions (vi)MPI interface for large-scale mass table calculations.Comment: 29 pages, 3 figures, 4 tables; Submitted to Computer Physics Communication

Calculation of Massless Feynman Integrals using Harmonic Sums

A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums. Algorithms for the evaluation of nested and harmonic sums are used to reduce the expressions to get analytical or numerical results for the expansion coefficients. Methods to increase the precision of numerical results are discussed.Comment: 30 pages, 6 figures; Minor typos corrected, references added. Published in Computer Physics Communication

Application of multisection recursive convolution in 3D FETD-FABC simulations

The multisection recursive convolution (MS-RC) methodology is successfully applied to the finite element time domain floquet absorbing boundary condition modeling of doubly periodic structures. It is shown that late time instability, can be delayed by improving the accuracy of RC and it can be effectively avoided by employing extrapolation

A Nonlinear Least Squares Fit procedure for analysis of immittance data of electrochemical systems

A Nonlinear Least Squares Fit (NLLSF) program is described, with which frequency dispersion data of electrochemical systems can be analyzed in terms of an equivalent circuit. The NLLSF procedure uses a combination of an analytical and gradient search according to the Marquardt algorithm. Through the use of an unique Circuit Description Code (CDC) different equivalent circuits may be used with the program. The use of an analytical derivatives routine enhances the execution speed. The power of such a fit procedure is demonstrated in multi parameter fits, on synthetic and real data, performed by the program “EQIVCT”