Optimized signal deduction procedure for the MIEZE spectroscopy technique

A method is reported to determine the phase and amplitude of sinusoidally modulated event rates, binned into four bins per oscillation, based on data generated at the resonant neutron spin-echo spectrometer RESEDA at FRM-II. The presented algorithm relies on a reconstruction of the unknown parameters. It omits a calculation-intensive fitting procedure and avoids contrast reduction due to averaging effects. It allows the current data acquisition bottleneck at RESEDA to be relaxed by a factor of four and thus increases the potential time resolution of the detector by the same factor. The approach is explained in detail and compared with the established fitting procedures of time series having four and 16 time bins per oscillation. In addition the empirical estimates of the errors of the three methods are presented and compared with each other. The reconstruction is shown to be unbiased, asymptotic and efficient for estimating the phase. Reconstructing the contrast increases the error bars by roughly 10% as compared with fitting 16 time-binned oscillations. Finally, the paper gives heuristic, analytical equations to estimate the error for phase and contrast as a function of their initial values and counting statistics.

Full counting statistics for interacting trapped fermions

We study NN spinless fermions in their ground state confined by an external potential in one dimension with long range interactions of the general Calogero-Sutherland type. For some choices of the potential this system maps to standard random matrix ensembles for general values of the Dyson index \betaβ. In the fermion model \betaβ controls the strength of the interaction, \beta=2β=2 corresponding to the noninteracting case. We study the quantum fluctuations of the number of fermions N_DND in a domain DD of macroscopic size in the bulk of the Fermi gas. We predict that for general \betaβ the variance of N_DND grows as A_{\beta} \log N + B_{\beta}AβlogN+Bβ for N \gg 1N≫1 and we obtain a formula for A_\betaAβ and B_\betaBβ. This is based on an explicit calculation for \beta\in\left\{ 1,2,4\right\}β∈{1,2,4} and on a conjecture that we formulate for general \betaβ. This conjecture further allows us to obtain a universal formula for the higher cumulants of N_DND. Our results for the variance in the microscopic regime are found to be consistent with the predictions of the Luttinger liquid theory with parameter K = 2/\betaK=2/β, and allow to go beyond. In addition we present families of interacting fermion models in one dimension which, in their ground states, can be mapped onto random matrix models. We obtain the mean fermion density for these models for general interaction parameter \betaβ. In some cases the fermion density exhibits interesting transitions, for example we obtain a noninteracting fermion formulation of the Gross-Witten-Wadia model.

Photon counting statistics with imperfect detectors

Measurement of photon statistics is an important tool for the verification of quantum properties of light. Due to the various imperfections of real single photon detectors, the observed statistics of photon counts deviates from the underlying statistics of photons. Here we analyze statistical properties of coherent states, and investigate a connection between Poissonian distribution of photons and sub-Poissonian distribution of photon counts due to the detector dead-time corrections. We derive a functional dependence between the mean number of photons and the mean number of photon counts, as well as connection between higher-order statistical moments, for the pulsed or continuous wave coherent light sources, and confirm the results by numerical simulations.

Resolution-intensity optimisation on quasielastic neutron scattering spectrometers

In quasieleastic neutron scattering spectrometers one usually faces a trade-off between energy resolution and counting statistics. If the resolution is improved the intensity at the detectors reduces and vice versa. It is not immediately clear how to weigh both factors against each other. In this paper it is proposed to use the maximum time obtainable by Fourier transform of the spectra as the quantity to be optimised. It is shown that this leads to a well-defined criterion for the choice of the resolution.

Trace-element XAFS sensitivity: a stress test for a new XRF multi-detector

X-ray absorption fine-structure (XAFS) spectroscopy can assess the chemical speciation of the elements providing their coordination and oxidation state, information generally hidden to other techniques. In the case of trace elements, achieving a good quality XAFS signal poses several challenges, as it requires high photon flux, counting statistics and detector linearity. Here, a new multi-element X-ray fluorescence detector is presented, specifically designed to probe the chemical speciation of trace 3d elements down to the p.p.m. range. The potentialities of the detector are presented through a case study: the speciation of ultra-diluted elements (Fe, Mn and Cr) in geological rocks from a calcareous formation related to the dispersal processes from Ontong (Java) volcanism (mid-Cretaceous). Trace-elements speciation is crucial in evaluating the impact of geogenic and anthropogenic harmful metals on the environment, and to evaluate the risks to human health and ecosystems. These results show that the new detector is suitable for collecting spectra of 3d elements in trace amounts in a calcareous matrix. The data quality is high enough that quantitative data analysis could be performed to determine their chemical speciation.

On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees

Tree shape statistics provide valuable quantitative insights into evolutionary mechanisms underpinning phylogenetic trees, a commonly used graph representation of evolutionary relationships among taxonomic units ranging from viruses to species. We study two subtree counting statistics, the number of cherries and the number of pitchforks, for random phylogenetic trees generated by two widely used null tree models: the proportional to distinguishable arrangements (PDA) and the Yule-Harding-Kingman (YHK) models. By developing limit theorems for a version of extended Pólya urn models in which negative entries are permitted for their replacement matrices, we deduce the strong laws of large numbers and the central limit theorems for the joint distributions of these two counting statistics for the PDA and the YHK models. Our results indicate that the limiting behaviour of these two statistics, when appropriately scaled using the number of leaves in the underlying trees, is independent of the initial tree used in the tree generating process.

Statistical Scrutiny of Particle Spectra in ep Collisions

Charged particle multiplicity distributions in positron–proton deep inelastic scattering at a centre-of-mass energy s = 300 GeV, measured in the hadronic centre-of-mass frames and in different pseudorapidity windows are studied in the framework of two statistical distributions, the shifted Gompertz distribution and the Weibull distribution. Normalised moments, normalised factorial moments and the H-moments of the multiplicity distributions are determined. The phenomenon of oscillatory behaviour of the counting statistics and the Koba-Nielsen-Olesen (KNO) scaling behaviour are investigated. This is the first such analysis using these data. In addition, projections of the two distributions for the expected average charged multiplicities obtainable at the proposed future ep colliders.

Study of LEAP® 5000 Deadtime and Precision via Silicon Pre-Sharpened-Microtip™ Standard Specimens

Atom probe tomography (APT) is a technique that has expanded significantly in terms of adoption, dataset size, and quality during the past 15 years. The sophistication used to ensure ultimate analysis precision has not kept pace. The earliest APT datasets were small enough that deadtime and background considerations for processing mass spectrum peaks were secondary. Today, datasets can reach beyond a billion atoms so that high precision data processing procedures and corrections need to be considered to attain reliable accuracy at the parts-per-million level. This paper considers options for mass spectrum ranging, deadtime corrections, and error propagation as applied to an extrinsic-silicon standard specimen to attain agreement for silicon isotopic fraction measurements across multiple instruments, instrument types, and acquisition conditions. Precision consistent with those predicted by counting statistics is attained showing agreement in silicon isotope fraction measurements across multiple instruments, instrument platforms, and analysis conditions.