H\"older equicontinuity of the integrated density of states at weak disorder

H\"older continuity, $|N_\lambda(E)-N_\lambda(E')|\le C |E-E'|^\alpha$, with a constant $C$ independent of the disorder strength $\lambda$ is proved for the integrated density of states $N_\lambda(E)$ associated to a discrete random operator $H = H_o + \lambda V$ consisting of a translation invariant hopping matrix $H_o$ and i.i.d. single site potentials $V$ with an absolutely continuous distribution, under a regularity assumption for the hopping term.Comment: 15 Pages, typos corrected, comments and ref. [1] added, theorems 3,4 combine

A room temperature 19-channel magnetic field mapping device for cardiac signals

We present a multichannel cardiac magnetic field imaging system built in Fribourg from optical double-resonance Cs vapor magnetometers. It consists of 25 individual sensors designed to record magnetic field maps of the beating human heart by simultaneous measurements on a grid of 19 points over the chest. The system is operated as an array of second order gradiometers using sophisticated digitally controlled feedback loops.Comment: 3 pages, 3 figures, submitted to Applied Physics Letter

Diffusion of wave packets in a Markov random potential

We consider the evolution of a tight binding wave packet propagating in a time dependent potential. If the potential evolves according to a stationary Markov process, we show that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.Comment: 19 pages, acknowledgments added and typos correcte

A high-sensitivity laser-pumped Mx magnetometer

Abstract.: We discuss the design and performance of a laser-pumped cesium vapor magnetometer in the Mx configuration. The device will be employed in the control and stabilization of fluctuating magnetic fields and gradients in a new experiment searching for a permanent electric dipole moment of the neutron. We have determined the intrinsic sensitivity of the device to be 15 fT in a 1 Hz bandwidth, limited by technical laser noise. In the shot noise limit the magnetometer can reach a sensitivity of 10 fT in a 1 Hz bandwidth. We have used the device to study the fluctuations of a stable magnetic field in a multi-layer magnetic shield for integration times in the range of 2-100 seconds. The residual fluctuations for times up to a few minutes are traced back to the instability of the power supply used to generate the fiel

The Influence of the Degree of Heterogeneity on the Elastic Properties of Random Sphere Packings

The macroscopic mechanical properties of colloidal particle gels strongly depend on the local arrangement of the powder particles. Experiments have shown that more heterogeneous microstructures exhibit up to one order of magnitude higher elastic properties than their more homogeneous counterparts at equal volume fraction. In this paper, packings of spherical particles are used as model structures to computationally investigate the elastic properties of coagulated particle gels as a function of their degree of heterogeneity. The discrete element model comprises a linear elastic contact law, particle bonding and damping. The simulation parameters were calibrated using a homogeneous and a heterogeneous microstructure originating from earlier Brownian dynamics simulations. A systematic study of the elastic properties as a function of the degree of heterogeneity was performed using two sets of microstructures obtained from Brownian dynamics simulation and from the void expansion method. Both sets cover a broad and to a large extent overlapping range of degrees of heterogeneity. The simulations have shown that the elastic properties as a function of the degree of heterogeneity are independent of the structure generation algorithm and that the relation between the shear modulus and the degree of heterogeneity can be well described by a power law. This suggests the presence of a critical degree of heterogeneity and, therefore, a phase transition between a phase with finite and one with zero elastic properties.Comment: 8 pages, 6 figures; Granular Matter (published online: 11. February 2012

Diffusive propagation of wave packets in a fluctuating periodic potential

We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a stationary Markov process satisfying certain technical criteria, we show that the square amplitude of the wave packet after diffusive rescaling converges to a superposition of solutions of a heat equation.Comment: 13 pages (v2: added a paragraph on the history of the problem, added some references, correct a few typos; v3 minor corrections, added keywords and subject classes

New gas mixtures suitable for rare event detection using a Micromegas-TPC detector

The aim of the presented work was to develop further techniques based on a Micromegas-TPC, in order to reach a high gas gain with good energy resolution, and to search for gas mixtures suitable for rare event detection. This paper focuses on xenon, which is convenient for the search of neutrinoless double beta decay in 136 Xe. Conversely, a small admixture of xenon to CF 4 can reduce attachment in the latter. This gas mixture would be suitable for dark matter searches and the study of solar and reactor neutrinos. Various configurations of the Micromegas plane were investigated and are described.Comment: 14 pages, 8 figures, article, revised version with improved figures, text modifications, accepted for publication by JINS

Delocalization and Diffusion Profile for Random Band Matrices

We consider Hermitian and symmetric random band matrices $H = (h_{xy})$ in $d \geq 1$ dimensions. The matrix entries $h_{xy}$, indexed by x,y \in (\bZ/L\bZ)^d, are independent, centred random variables with variances s_{xy} = \E |h_{xy}|^2. We assume that $s_{xy}$ is negligible if $|x-y|$ exceeds the band width $W$. In one dimension we prove that the eigenvectors of $H$ are delocalized if $W\gg L^{4/5}$. We also show that the magnitude of the matrix entries \abs{G_{xy}}^2 of the resolvent $G=G(z)=(H-z)^{-1}$ is self-averaging and we compute \E \abs{G_{xy}}^2. We show that, as $L\to\infty$ and $W\gg L^{4/5}$, the behaviour of \E |G_{xy}|^2 is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions

Generation of folk song melodies using Bayes transforms

The paper introduces the `Bayes transform', a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transforms can be the means of determining the repetition hierarchy of note sequences (melodies) in an empirical and domain-general way. The paper investigates application of this approach to Folk Song, examining the results that can be obtained by treating such transforms as generative models