Spectral fluctuations of tridiagonal random matrices from the beta-Hermite ensemble

A time series delta(n), the fluctuation of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of NxN random matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble as a function of beta (zero or positive) by Monte Carlo simulations. The fluctuation of delta(n) and the autocorrelation function vary logarithmically with n for any beta>0 (1<<n<<N). The simple logarithmic behavior reported for the higher-order moments of delta(n) for the GOE (beta=1) and the GUE (beta=2) is valid for any positive beta and is accounted for by Gaussian distributions whose variances depend linearly on ln(n). The 1/f noise previously demonstrated for delta(n) series of the three Gaussian ensembles, is characterized by wavelet analysis both as a function of beta and of N. When beta decreases from 1 to 0, for a given and large enough N, the evolution from a 1/f noise at beta=1 to a 1/f^2 noise at beta=0 is heterogeneous with a ~1/f^2 noise at the finest scales and a ~1/f noise at the coarsest ones. The range of scales in which a ~1/f^2 noise predominates grows progressively when beta decreases. Asymptotically, a 1/f^2 noise is found for beta=0 while a 1/f noise is the rule for beta positive.Comment: 35 pages, 10 figures, corresponding author: G. Le Cae

Nonperturbative QED Processes at ELI-NP

The present paper analyses the current results and pursuits the main steps required for the design of SF-QED experiments at High-Power Laser System (HPLS) of ELI-NP in Magurele, Romania. After a brief analysis of the first experiment (E-144 SLAC), which confirmed the existence of non-linear QED interactions of the high energy electrons with the photons of a laser beam, we went on to present fundamental QED processes possible to be studied at ELI-NP in a multi-photon regime. The kinematics and characteristic parameters of the laser beam interacting with electrons were presented. In the preparation of an experiment at ELI-NP, the analysis of the kinematics and dynamics of the non-linear QED interaction processes with the physical vacuum are required. Initially, the linear QED processes and the corresponding Feynman diagrams that allow to determine the amplitude of these processes are reviewed. Based on these amplitudes, the cross sections of the processes can be obtained. For multi-photon interactions it is necessary to adapt the technique of Feynman diagrams from linear QED processes to the non-linear ones, by moving to the quantum field description with dressed Dirac-Volkov states, for particles in intense EM field. They then allow evaluation of the amplitude of the physical processes and ultimately the determination of the corresponding cross section. The SF-QED processes of multi-photon interactions with strong laser fields, can be done taking into account the characteristics of the existing facilities at ELI-NP in the context of the experimental production of electron-positron-pairs and of energetic gamma-rays. We show also some upcoming experiments similar to ours, in various stages of preparation.Comment: Presented at Bucharest University Meeting 2023 https://ssffb.fizica.unibuc.ro/SSFFB/Section.php?SectID=22

Functionalized coatings by electrospinning for anti-oxidant food packaging

The development of advanced formulations used for food packaging applications, which behave as protection or preservation materials and improve consumers’ health offers a route to reduced food wastage. The present study deals with investigations on the possibility of obtaining functionalized coatings by electrospinning of poly(ɛ-caprolactone), a synthetic biodegradable polymer together with vitamin E (α-tocopherol), selected as plant-based phenolic antioxidant. In this approach electrospinning allows the production of high surface area materials and thus offering an increased antioxidant activity. The electrospun fibres of poly(ɛ-caprolactone)/vitamin E were obtained, studied and their antioxidant properties were evaluated by measuring the fibre reactivity with 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical. The potential for extending the shelf-life of food products by using this approach is discussed

Global spectrum fluctuations for the β\beta-Hermite and β\beta-Laguerre ensembles via matrix models

We study the global spectrum fluctuations for $\beta$-Hermite and $\beta$-Laguerre ensembles via the tridiagonal matrix models introduced in \cite{dumitriu02}, and prove that the fluctuations describe a Gaussian process on monomials. We extend our results to slightly larger classes of random matrices.Comment: 43 pages, 2 figures; typos correcte

Antioxidant activity, phenolic compounds and colour of red wines treated with new fining agents

Nowadays the clarification and stabilization of red wines is generally done with conventional fining agents, like bentonite and activated coal, which pose a major challenge to environmental security and wastes management. This stimulated the use of many new techniques in order to discover alternative fining agents that don’t have negative influence on color, phenolic compounds and quality parameters. The aim of this research is to determine, how alternative fining agents, in different doses, affect antioxidant activity and colour parameters of 'Cabernet Sauvignon' red wines. Experimental material is from North-East Romania and was fined with mesoporous materials, bentonite and activated coal. Discriminant analysis classified 'Cabernet Sauvignon' wines according to the different fining agents based on total polyphenolic compounds and total antioxidant activity. Alternative fining agents, as mesoporous materials, have less impact on the colour and phenolic content of red wines in contrast to activated coal and bentonite treatments that can conduct to unsatisfying characteristics. Mesoporous materials are preferable and could be an exceptional adsorbent for polyphenolic compounds

Ab initio calculation of the 66 low lying electronic states of HeH+^+: adiabatic and diabatic representations

We present an ab initio study of the HeH$^+$ molecule. Using the quantum chemistry package MOLPRO and a large adapted basis set, we have calculated the adiabatic potential energy curves of the first 20 $^1 \Sigma^+$, 19 $^3\Sigma^+$, 12 $^1\Pi$, 9 $^3\Pi$, 4 $^1\Delta$ and 2 $^3\Delta$ electronic states of the ion in CASSCF and CI approaches. The results are compared with previous works. The radial and rotational non-adiabatic coupling matrix elements as well as the dipole moments are also calculated. The asymptotic behaviour of the potential energy curves and of the various couplings between the states is also studied. Using the radial couplings, the diabatic representation is defined and we present an example of our diabatization procedure on the $^1\Sigma^+$ states.Comment: v2. Minor text changes. 28 pages, 18 figures. accepted in J. Phys.

Calculation of Atomic Data for NASA Missions

The interpretation of cosmic spectra relies on a vast sea of atomic data which are not readily obtainable from analytic expressions or simple calculations. Rather, their evaluation typically requires state-of-the-art atomic physics calculations, with the inclusion of weaker effects (spin-orbit and configuration interactions, relaxation, Auger broadening, etc.), to achieve the level of accuracy needed for use by astrophysicists. Our NASA-supported research program is focused on calculating data for three important atomic processes, 1) dielectronic recombination (DR), 2) inner-shell photoabsorption, and 3) fluorescence and Auger decay of inner-shell vacancy states. Some additional details and examples of our recent findings are given below

Fast linear algebra is stable

In an earlier paper, we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of $n$-by-$n$ matrices can be done by any algorithm in $O(n^{\omega + \eta})$ operations for any $\eta > 0$, then it can be done stably in $O(n^{\omega + \eta})$ operations for any $\eta > 0$. Here we extend this result to show that essentially all standard linear algebra operations, including LU decomposition, QR decomposition, linear equation solving, matrix inversion, solving least squares problems, (generalized) eigenvalue problems and the singular value decomposition can also be done stably (in a normwise sense) in $O(n^{\omega + \eta})$ operations.Comment: 26 pages; final version; to appear in Numerische Mathemati

Shape resonances in K -shell photodetachment of small size-selected clusters: Experiment and theory

K-shell photodetachment of size-selected B(2)(-) and B(3)(-) cluster anions has been measured and calculated. The experimental absolute photodetachment cross sections exhibit bound resonances below threshold and two shape resonances above the K-shell threshold. Similar results were obtained for all of the cationic products observed, B(+) and B(2)(+) from B(2)(-), as well as B(+), B(2)(+), and B(3)(+) from B(3)(-). The overall agreement between measured and calculated photodetachment cross sections is very good. However, the theoretical study yielded additional bound resonances not observed in the experimental data