Dirac Equation with External Potential and Initial Data on Cauchy Surfaces

With this paper we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincar\'e group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove convenient Paley-Wiener- and Sobolev-type estimates. These generalized Fourier transforms immediately allow the construction of a unitary evolution operator for the free Dirac equation between the Hilbert spaces of square-integrable wave functions of two respective Cauchy surfaces. With a Picard-Lindel\"of argument this evolution map is generalized to the Dirac evolution including the external potential. For the latter we introduce a convenient interaction picture on Cauchy surfaces. These tools immediately provide another proof of the well-known existence and uniqueness of classical solutions and their causal structure

Linearly edge-reinforced random walks

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the random walk on infinite graphs. On trees, one has a representation as a random walk in an independent random environment. We review recent results for the random walk on ladders: recurrence, a representation as a random walk in a random environment, and estimates for the position of the random walker.Comment: Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

ATLAS Monitored Drift Tube Chambers in E = 11 MeV Neutron Background

The influence of fast neutrons on the occupancy and the single tube resolution of ATLAS muon drift detectors was investigated by exposing a chamber built out of 3 layers of 3 short standard drift tubes to neutron flux-densities of up to 16 kHz/cm2 at a neutron energy of E=11 MeV. Pulse shape capable NE213 scintillaton detectors and a calibrated BF3 neutron detector provided monitoring of the neutron flux-density and energy. The sensitivity of the drift chamber to the neutrons was measured to be 4*10-4 by comparing data sets with and without neutron background. For the investigation of tracks of cosmic muons two silicon-strip detectors above and underneath the chamber allow to compare measured drift-radii with reference tracks. Alternatively, the single tube resolution was determined using the triple-sum method. The comparison between data with and without neutron irradiation shows only a marginal effect on the resolution and little influence on the muon track reconstruction.Comment: 4 pages, 11 figures, conferenc

Spatially resolved spectroscopy of Coma cluster early-type galaxies - II:the minor axis dataset

We present minor axis, off set major axis and one diagonal long slit spectra for 10 E and S0 galaxies of the Coma cluster drawn from a magnitude-limited sample studied before. We derive rotation curves, velocity dispersion profiles and the H-3 and H-4 coefficients of the Hermite decomposition of the line of sight velocity distribution. Moreover, we derive the line index profiles of Mg, Fe and Hbeta line indices and assess their errors. The data will be used to construct dynamical models of the galaxies and study their stellar populations

From Anderson to anomalous localization in cold atomic gases with effective spin-orbit coupling

We study the dynamics of a one-dimensional spin-orbit coupled Schrodinger particle with two internal components moving in a random potential. We show that this model can be implemented by the interaction of cold atoms with external lasers and additional Zeeman and Stark shifts. By direct numerical simulations a crossover from an exponential Anderson-type localization to an anomalous power-law behavior of the intensity correlation is found when the spin-orbit coupling becomes large. The power-law behavior is connected to a Dyson singularity in the density of states emerging at zero energy when the system approaches the quasi-relativistic limit of the random mass Dirac model. We discuss conditions under which the crossover is observable in an experiment with ultracold atoms and construct explicitly the zero-energy state, thus proving its existence under proper conditions.Comment: 4 pages and 4 figure

Random walks in random Dirichlet environment are transient in dimension d≥3d\ge 3

We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On $\Z^d$, RWDE are parameterized by a $2d$-uplet of positive reals. We prove that for all values of the parameters, RWDE are transient in dimension $d\ge 3$. We also prove that the Green function has some finite moments and we characterize the finite moments. Our result is more general and applies for example to finitely generated symmetric transient Cayley graphs. In terms of reinforced random walks it implies that directed edge reinforced random walks are transient for $d\ge 3$.Comment: New version published at PTRF with an analytic proof of lemma

Relativistic quantum effects of Dirac particles simulated by ultracold atoms

Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.Comment: 22 pages, review article in Frontiers of Physics: Proceedings on Quantum Dynamics of Ultracold Atom

Impression management and retrospective sense-making in corporate annual reports: banks' graphical reporting during the global financial crisis

This study investigates two potentially complementary reporting scenarios in annual reports: reactive impression management and retrospective sense-making. It examines stock market performance graphs in European listed banks? annual reports before and during the global financial crisis. Our results indicate that banks reacted to the global financial crisis by omitting stock market performance graphs from the annual report and from its most prominent sections. On the other hand, banks reduced favorable distortions and favorable performance comparisons. No significant evidence of retrospective sense-making is found. Overall, the findings are consistent with impression management incorporating human cognitive biases, with companies preferring misrepresentation by omission over misrepresentation by commission. Under high public scrutiny, banks appear to seek to provide a more favorable view by concealing negative information rather than by favorable distortions or comparisons. The study contributes to the development of impression management theories. It uses a psychological interpretation that incorporates human cognitive biases, rather than adopting a purely economically based perspective