Transport of covariance matrices in the inhomogeneous magnetic field of the ATLAS experiment by the application of a semi-analytical method

In this paper we study the transport of track parameter covariance matrices - the so-called error propagation - in the inhomogeneous magnetic field of the ATLAS experiment. The Jacobian elements are transported in parallel with the track parameters, avoiding the inherent need of any purely numerical scheme of propagating a set of auxiliary tracks. We evaluate the quality of the transported Jacobians by a very thorough, purely numerical approach of obtaining the same derivatives, providing a quantitative understanding of the effects of including gradients of energy loss and the magnetic field on the accuracy of the error propagation. Irrespective of the accuracy of the underlying track parameter propagation, the method of parallel integration of the derivatives is demonstrated to be significantly faster than even the simplest numerical scheme. The error propagation presented in this paper is part of the simultaneous track and error propagation (STEP) algorithm of the common ATLAS tracking software

Track parameter propagation through the application of a new adaptive Runge-Kutta-Nystrom method in the ATLAS experiment

In this paper we study several fixed step and adaptive Runge-Kutta methods suitable for transporting track parameters through an inhomogeneous magnetic field. Moreover, we present a new adaptive Runge-Kutta-Nystrom method which estimates the local error of the extrapolation without introducing extra stages to the original Runge-Kutta-Nystrom method. Furthermore, these methods are compared for propagation accuracy and computing cost efficiency in the simultaneous track and error propagation (STEP) algorithm of the common ATLAS tracking software. The tests show the new adaptive Runge-Kutta-Nystrom method to be the most computing cost efficient

Excitonic effects in solids described by time-dependent density functional theory

Starting from the many-body Bethe-Salpeter equation we derive an exchange-correlation kernel $f_{xc}$ that reproduces excitonic effects in bulk materials within time-dependent density functional theory. The resulting $f_{xc}$ accounts for both self-energy corrections and the electron-hole interaction. It is {\em static}, {\em non-local} and has a long-range Coulomb tail. Taking the example of bulk silicon, we show that the $- \alpha / q^2$ divergency is crucial and can, in the case of continuum excitons, even be sufficient for reproducing the excitonic effects and yielding excellent agreement between the calculated and the experimental absorption spectrum.Comment: 6 pages, 1 figur

A real-space, rela-time method for the dielectric function

We present an algorithm to calculate the linear response of periodic systems in the time-dependent density functional thoery, using a real-space representation of the electron wave functions and calculating the dynamics in real time. The real-space formulation increases the efficiency for calculating the interaction, and the real-time treatment decreases storage requirements and the allows the entire frequency-dependent response to be calculated at once. We give as examples the dielectric functions of a simple metal, lithium, and an elemental insulator, diamond.Comment: 17 pages, Latex, 5 figure