Abstract:
The propagation of electrons in static and uniform electromagnetic fields is a standard topic of classical electrodynamics. The Hamilton function is given by a quadratic polynomial in the positions and momenta. The corresponding quantum-mechanical problem has been analyzed in great detail and the eigenfunctions and time evolution operators are well-known. Surprisingly, the energy-dependent counterpart of the time-evolution operator, the Green function, is not easily accessible. However in many situations one is interested in the evolution of a system that started with emitted particles that carry a specific energy. In the following we present a suitable approach to study this type of matter waves arising from a localized region in space. Two applications are discussed, the photodetachment current in external fields and the quantum Hall effect in a fermionic electron gas.

Abstract:
It is evident that a lot of accidents occur because of drowsiness or inattentiveness of the driver. The logical consequence is that we have to find methods to better analyze the driver. A lot of research has been spent on camera-based systems which focus on the driver's eye gaze or his head movement. But there are few systems that provide camera-free driver analyzing. This is the main goal of the work presented here which is structured in three phases, with the operational goal of having a working driver analyzer implemented in a car. The main question is: is it possible to make statements concerning the driver and his state by using vehicle data from the CAN Bus only? This paper describes the current state of driver analyzing, our overall system architecture, as well as future work. At the moment, we focus on detecting the driving style of a person. 1. Introduction Driver analysis (DA) has been an active field of research for years. For example, [1] published an article about driver monitoring already in 2005. Among others, DA can be divided in the following subtopics: driver monitoring, driving style analysis, and merging vehicle data to derive conclusions concerning the driver (The word driver means both, female as well as male drivers. This is also relevant for words like “his” or “him” which reflect also both, female as well as male persons.) and his environment. For our research work, we focus on the following aspects. (i)How can the state of the driver be detected without using a camera or realtime biosensor data like a electrocardiogram (ecd)? (ii)How can we support the driver, depending on his actual driving situation, based on the results of the driver state detection? Driver monitoring is usually performed by cameras installed in the car for detecting the driver's behavior or state, mostly by using infrared cameras ([2, 3], or [1]). There are also first results for noncamera based research on driver analysis: By analyzing analog speed graphs, Rygula [4] makes conclusions about the driving style, speed profile and, depending on driving time and course, aggressiveness of the driver. Therefore, he evaluated ten analog speed graphs for two drivers by comparing their speed profile, their profile referring to the distance, or referring to route and direction. Rygula states that “Even a brake of 45 minutes reduce aggressivity of driving style” ([4, page 79]). A different approach is the research on context recognition in vehicles and the development of a driver model. Ferscha and Riener [5] describe this process of in-car context recognition and

Abstract:
We investigate the impact of finite volume effects on the critical number of flavours, N_f^c, for chiral symmetry restoration in QED3. To this end we solve a set of coupled Dyson-Schwinger equations on a torus. For order parameters such as the anomalous dimension of the fermion wave function or the chiral condensate we find substantial evidence for a large dependence on the volume. We observe a shift in N_f^c from values in the range of 3.61 \le N_f^c \le 3.84 in the infinite volume/continuum limit down to values below N_f \le 1.5 at finite volumes in agreement with earlier results of Gusynin and Reenders in a simpler truncation scheme. These findings explain discrepancies in N_f^c between continuum and lattice studies.

Abstract:
We summarize our recent results for the quark loop part of the light-by-light scattering contribution as well as the hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon. In particular we focus on the role played by the momentum dependence of the quark- and quark-photon vertex dressing functions. We give a detailed comparison of the Dyson-Schwinger description of this contribution to the corresponding picture emerging from hadronic models in particular the extended Nambu--Jona-Lasonio model (ENJL). We find that the details of the momentum dependence are important on a quantitative level. Especially the transverse parts of the quark-photon-vertex, which serve as a dynamical extension of simple vector meson dominance models, do not yield the large suppression of the light-by-light contribution found in the ENJL model if realistic dressings are taken into account.

Abstract:
We summarise recent results for the quark loop part of the light-by-light scattering contribution to the muons anomalous magnetic moment. In particular we focus on the impact of a momentum dependent quark and quark-photon vertex. We compare the Dyson-Schwinger description with that of the extended Nambu--Jona-Lasinio model (ENJL) and find important quantitative differences. In particular the transverse parts of the quark-photon-vertex, which serve as a dynamical extension of simple vector meson dominance models, do not yield the large suppression as found in the ENJL model.

Abstract:
We investigate photodetachment from negative ions in a homogeneous 1.0-T magnetic field and a parallel electric field of approximately 10 V/cm. A theoretical model for detachment in combined fields is presented. Calculations show that a field of 10 V/cm or more should considerably diminish the Landau structure in the detachment cross section. The ions are produced and stored in a Penning ion trap and illuminated by a single-mode dye laser. We present preliminary results for detachment from S- showing qualitative agreement with the model. Future directions of the work are also discussed.

Abstract:
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors a rich set of features which find their interpretation in the unusual and interesting properties of the classical motion of the electrons: For instance, the number of interfering trajectories can be adjusted in this system, and the turning surfaces of classical motion contain a complex array of singularities. We perform a comprehensive analysis of both the semiclassical approximation and the quantum solution, and we make predictions that should serve as a guide for future photodetachment experiments.

Abstract:
We investigate the impact of finite volume effects on the critical number of flavours, N_f^c, for chiral symmetry restoration in QED3. To this end we solve a set of coupled Dyson-Schwinger equations on a torus. For order parameters such as the anomalous dimension of the fermion wave function or the chiral condensate we find substantial evidence for a large dependence on the volume. We observe a shift in N_f^c from values in the range of 3.61 \le N_f^c \le 3.84 in the infinite volume/continuum limit down to values below N_f \le 1.5 at finite volumes in agreement with earlier results of Gusynin and Reenders in a simpler truncation scheme. These findings explain discrepancies in N_f^c between continuum and lattice studies.

Abstract:
An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and introduce pointlike multipole sources as their limiting case. Partial wave theory is recovered for freely propagating particles. We obtain novel results for ballistic scattering in an external uniform force field, where we provide analytical solutions for both the scattering waves and the integrated particle flux. Our theory directly applies to p-wave photodetachment in an electric field. Furthermore, illustrating the effects of extended sources, we predict some properties of vortex-bearing atom laser beams outcoupled from a rotating Bose-Einstein condensate under the influence of gravity.

Abstract:
We present a calculation of the hadronic vacuum polarization (HVP) tensor within the framework of Dyson--Schwinger equations. To this end we use a well-established phenomenological model for the quark-gluon interaction with parameters fixed to reproduce hadronic observables. From the HVP tensor we compute both the Adler function and the HVP contribution to the anomalous magnetic moment of the muon, $a_\mu$. We find $a_\mu^{HVP}= 6760\times 10^{-11}$ which deviates about two percent from the value extracted from experiment. Additionally, we make comparison with a recent lattice determination of $a_\mu^{HVP}$ and find good agreement within our approach. We also discuss the implications of our result for a corresponding calculation of the hadronic light-by-light scattering contribution to $a_\mu$.