More efficient computation of the complex error function

Gautschi has developed an algorithm that calculates the value of the Faddeeva function w(z) for a given complex number z in the first quadrant, up to 10 significant digits. We show that by modifying the tuning of the algorithm and testing the relative rather than the absolute error we can improve the accuracy of this algorithm to 14 significant digits throughout almost the whole of the complex plane, as well as increase its speed significantly in most of the complex plane. The efficiency of the calculation is further enhanced by using a different approximation in the neighborhood of the origin, where the Gautschi algorithm becomes ineffective. Finally, we develop a criterion to test the reliability of the algorithm's results near the zeros of the function, which occur in the third and fourth quadrants

Reconstructions of the Ge(0 0 1) surface

We have performed dipole calculations of energies of the Ge(0 0 1) surface to compare the ground states of b(2 × 1), c(4 × 2), p(2 × 2) and p(4 × 1) symmetry dimer reconstructions. We have found that p(2 × 2) is the lowest energy reconstruction at zero temperature

Equivalence between the real time Feynman histories and the quantum shutter approaches for the "passage time" in tunneling

We show the equivalence of the functions $G_{\rm p}(t)$ and $|\Psi(d,t)|^2$ for the ``passage time'' in tunneling. The former, obtained within the framework of the real time Feynman histories approach to the tunneling time problem, using the Gell-Mann and Hartle's decoherence functional, and the latter involving an exact analytical solution to the time-dependent Schr\"{o}dinger equation for cutoff initial waves

Generalization of the coupled dipole method to periodic structures

We present a generalization of the coupled dipole method to the scattering of light by arbitrary periodic structures. This new formulation of the coupled dipole method relies on the same direct-space discretization scheme that is widely used to study the scattering of light by finite objects. Therefore, all the knowledge acquired previously for finite systems can be transposed to the study of periodic structures.Comment: 5 pages, 2 figures, and 1 tabl

X-Ray Resonant Exchange Scattering from 3d Transition Metal Surfaces

Contains fulltext : 27987.pdf (publisher's version ) (Open Access

More efficient computation of the complex error function

Gautschi has developed an algorithm that calculates the value of the Faddeeva function w(z) for a given complex number z in the first quadrant, up to 10 significant digits. We show that by modifying the tuning of the algorithm and testing the relative rather than the absolute error we can improve the accuracy of this algorithm to 14 significant digits throughout almost the whole of the complex plane, as well as increase its speed significantly in most of the complex plane. The efficiency of the calculation is further enhanced by using a different approximation in the neighborhood of the origin, where the Gautschi algorithm becomes ineffective. Finally, we develop a criterion to test the reliability of the algorithm's results near the zeros of the function, which occur in the third and fourth quadrants