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

Aqueous Black Colloids of Reticular Nanostructured Gold

Since ancient times, noble gold has continuously contributed to several aspects of life from medicine to electronics. It perpetually reveals its new features. We report the finding of a unique form of gold, reticular nanostructured gold (RNG), as an aqueous black colloid, for which we present a one-step synthesis. The reticules consist of gold crystals that interconnect to form compact strands. RNG exhibits high conductivity and low reflection and these features, coupled with the high specific surface area of the material, could prove valuable for applications in electronics and catalysis. Due to high absorption throughout the visible and infrared domain, RNG has the potential to be applied in the construction of sensitive solar cells or as a substrate for Raman spectroscopy

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

Breaking quantum linearity: constraints from human perception and cosmological implications

Resolving the tension between quantum superpositions and the uniqueness of the classical world is a major open problem. One possibility, which is extensively explored both theoretically and experimentally, is that quantum linearity breaks above a given scale. Theoretically, this possibility is predicted by collapse models. They provide quantitative information on where violations of the superposition principle become manifest. Here we show that the lower bound on the collapse parameter lambda, coming from the analysis of the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than the original bound, in agreement with more recent analysis. This implies that the collapse becomes effective with systems containing ~ 10^4 - 10^5 nucleons, and thus falls within the range of testability with present-day technology. We also compare the spectrum of the collapsing field with those of known cosmological fields, showing that a typical cosmological random field can yield an efficient wave function collapse.Comment: 13 pages, LaTeX, 3 figure

Effects of Probiotic (Bifidobacterium longum 35624) Supplementation on Exercise Performance, Immune Modulation, and Cognitive Outlook in Division I Female Swimmers

This work is licensed under a Creative Commons Attribution 4.0 International License.Our aim was to determine the effects of probiotic supplementation (Bifidobacterium longum 35624; 1 billion CFU·d−1) on exercise performance, immune modulation, and cognitive outlook in collegiate female athletes during six weeks of offseason training. Seventeen National Collegiate Athletic Association (NCAA) Division 1 collegiate female swimmers participated in this two-group matched, double-blind, placebo controlled design. Via stratified randomization, participants were assigned to probiotic (B. longum 35624; n = 8) or placebo (n = 9) groups. Pre, mid, and post-training, all participants completed exercise performance testing (aerobic/anaerobic swim time trials and force plate vertical jump) as well as provided serum (cytokine and gastrointestinal inflammatory markers) and salivary immunoglobulin A samples. Recovery-stress questionnaire for athletes (RESTQ-Sport) was administered at baseline and conclusion of each week. Data were analyzed by analysis of covariance (ANCOVA) by time point with the respective baseline values of each dependent variable being the covariate. No significant differences in exercise performance and biochemical markers were observed between groups following offseason training. Recovery-Stress Questionnaire for Athletes (RESTQ-sport) values in B. longum 35624 group had significantly higher (i.e., more desired; p < 0.05) values in sport recovery (weeks five and six) than placebo. Probiotic supplementation in collegiate female swimmers did not affect exercise performance or immune function throughout offseason training, but did indicate alterations in cognitive outlook.Procter & Gamble, Cincinnati, OH, USA gran

The impact of seismic noise produced by wind turbines on seismic borehole measurements

Seismic signals produced by wind turbines can have an adverse effect on seismological measurements up to distances of several kilometres. Based on numerical simulations of the emitted seismic wave field, we study the effectivity of seismic borehole installations as a way to reduce the incoming noise. We analyse the signal amplitude as a function of sensor depth and investigate effects of seismic velocities, damping parameters and geological layering in the subsurface. Our numerical approach is validated by real data from borehole installations affected by wind turbines. We demonstrate that a seismic borehole installation with an adequate depth can effectively reduce the impact of seismic noise from wind turbines in comparison to surface installations. Therefore, placing the seismometer at greater depth represents a potentially effective measure to improve or retain the quality of the recordings at a seismic station. However, the advantages of the borehole decrease significantly with increasing signal wavelength.</p

Atomic-scale confinement of optical fields

In the presence of matter there is no fundamental limit preventing confinement of visible light even down to atomic scales. Achieving such confinement and the corresponding intensity enhancement inevitably requires simultaneous control over atomic-scale details of material structures and over the optical modes that such structures support. By means of self-assembly we have obtained side-by-side aligned gold nanorod dimers with robust atomically-defined gaps reaching below 0.5 nm. The existence of atomically-confined light fields in these gaps is demonstrated by observing extreme Coulomb splitting of corresponding symmetric and anti-symmetric dimer eigenmodes of more than 800 meV in white-light scattering experiments. Our results open new perspectives for atomically-resolved spectroscopic imaging, deeply nonlinear optics, ultra-sensing, cavity optomechanics as well as for the realization of novel quantum-optical devices

Structural characterization of the interaction of α-synuclein nascent chains with the ribosomal surface and trigger factor

The ribosome is increasingly becoming recognized as a key hub for integrating quality control processes associated with protein biosynthesis and cotranslational folding (CTF). The molecular mechanisms by which these processes take place, however, remain largely unknown, in particular in the case of intrinsically disordered proteins (IDPs). To address this question, we studied at a residue-specific level the structure and dynamics of ribosome-nascent chain complexes (RNCs) of α-synuclein (αSyn), an IDP associated with Parkinson’s disease (PD). Using solution-state nuclear magnetic resonance (NMR) spectroscopy and coarse-grained molecular dynamics (MD) simulations, we find that, although the nascent chain (NC) has a highly disordered conformation, its N-terminal region shows resonance broadening consistent with interactions involving specific regions of the ribosome surface. We also investigated the effects of the ribosome-associated molecular chaperone trigger factor (TF) on αSyn structure and dynamics using resonance broadening to define a footprint of the TF–RNC interactions. We have used these data to construct structural models that suggest specific ways by which emerging NCs can interact with the biosynthesis and quality control machinery