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

An investigation of the impact of data breach severity on the readability of mandatory data breach notification letters: evidence from U.S. firms

The aim of this article is to investigate the impact of data breach severity on the readability of mandatory data breach notification letters. Using a content analysis approach to determine data breach severity attributes (measured by the total number of breached records, type of data accessed, the source of the data breach, and how the data were used), in conjunction with readability measures (reading complexity, numerical intensity, length of letter, word size, and unique words), 512 data breach incidents from 281 U.S. firms across the 2012–2015 period were examined. The results indicate that data breach severity has a positive impact on reading complexity, length of letter, word size, and unique words, and a negative impact on numerical terms. Interpreting the results collectively through the lens of impression management, it can be inferred that business managers may be attempting to obfuscate bad news associated with high data breach severity incidents by manipulating syntactical features of the data breach notification letters in a way that makes the message difficult for individuals to comprehend. The study contributes to the information studies and impression management behavior literatures by analyzing linguistic cues in notifications following a data breach incident

Temperature Studies for ATLAS MDT BOS Chambers

Data sets with high statistics taken at the cosmic ray facility, equipped with 3 ATLAS BOS MDT chambers, in Garching (Munich) have been used to study temperature and pressure effects on gas gain and drifttime. The deformation of a thermally expanded chamber was reconstructed using the internal RasNik alignment monitoring system and the tracks from cosmic data. For these studies a heating system was designed to increase the temperature of the middle chamber by up to 20 Kelvins over room temperature. For comparison the temperature effects on gas properties have been simulated with Garfield. The maximum drifttime decreased under temperature raise by -2.21 +- 0.08 ns/K, in agreement with the results of pressure variations and the Garfield simulation. The increased temperatures led to a linear increase of the gas gain of about 2.1% 1/K. The chamber deformation has been analyzed with the help of reconstructed tracks. By the comparison of the tracks through the reference chambers with these through the test chamber the thermal expansion has been reconstructed and the result shows agreement with the theoretical expansion coefficient. As the wires are fixed at the end of the chamber, the wire position calculation can not provide a conclusion for the chamber middle. The complete deformation has been identified with the analysis of the monitoring system RasNik, whose measured values have shown a homogeneous expansion of the whole chamber, overlayed by a shift and a rotation of the chamber middle with respect to the outer part of the chamber. The established results of both methods are in agreement. We present as well a model for the position-drifttime correction as function of temperature.Comment: 4 pages, 12 figures, conferenc

Time Evolution of the External Field Problem in QED

We construct the time-evolution for the second quantized Dirac equation subject to a smooth, compactly supported, time dependent electromagnetic potential and identify the degrees of freedom involved. Earlier works on this (e.g. Ruijsenaars) observed the Shale-Stinespring condition and showed that the one-particle time-evolution can be lifted to Fock space if and only if the external field had zero magnetic components. We scrutinize the idea, observed earlier by Fierz and Scharf, that the time-evolution can be implemented between time varying Fock spaces. In order to define these Fock spaces we are led to consider classes of reference vacua and polarizations. We show that this implementation is up to a phase independent of the chosen reference vacuum or polarization and that all induced transition probabilities are well-defined and unique.Comment: 60 pages, 1 figure, revised introduction, summary of results added, typos correcte

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

Chiral confinement in quasirelativistic Bose-Einstein condensates

In the presence of a laser-induced spin-orbit coupling an interacting ultra cold spinor Bose-Einstein condensate may acquire a quasi-relativistic character described by a non-linear Dirac-like equation. We show that as a result of the spin-orbit coupling and the non-linearity the condensate may become self-trapped, resembling the so-called chiral confinement, previously studied in the context of the massive Thirring model. We first consider 1D geometries where the self-confined condensates present an intriguing sinusoidal dependence on the inter-particle interactions. We further show that multi-dimensional chiral-confinement is also possible under appropriate feasible laser arrangements, and discuss the properties of 2D and 3D condensates, which differ significantly from the 1D case.Comment: 4 page