Universality of a family of Random Matrix Ensembles with logarithmic soft-confinement potentials

Recently we introduced a family of $U(N)$ invariant Random Matrix Ensembles which is characterized by a parameter $\lambda$ describing logarithmic soft-confinement potentials $V(H) \sim [\ln H]^{(1+\lambda)} \:(\lambda>0$). We showed that we can study eigenvalue correlations of these "$\lambda$-ensembles" based on the numerical construction of the corresponding orthogonal polynomials with respect to the weight function $\exp[- (\ln x)^{1+\lambda}]$. In this work, we expand our previous work and show that: i) the eigenvalue density is given by a power-law of the form $\rho(x) \propto [\ln x]^{\lambda-1}/x$ and ii) the two-level kernel has an anomalous structure, which is characteristic of the critical ensembles. We further show that the anomalous part, or the so-called "ghost-correlation peak", is controlled by the parameter $\lambda$; decreasing $\lambda$ increases the anomaly. We also identify the two-level kernel of the $\lambda$-ensembles in the semiclassical regime, which can be written in a sinh-kernel form with more general argument that reduces to that of the critical ensembles for $\lambda=1$. Finally, we discuss the universality of the $\lambda$-ensembles, which includes Wigner-Dyson universality ($\lambda \to \infty$ limit), the uncorrelated Poisson-like behavior ($\lambda \to 0$ limit), and a critical behavior for all the intermediate $\lambda$ ($0<\lambda<\infty$) in the semiclassical regime. We also comment on the implications of our results in the context of the localization-delocalization problems as well as the $N$ dependence of the two-level kernel of the fat-tail random matrices.Comment: 10 pages, 13 figure

Laser ablation loading of a radiofrequency ion trap

The production of ions via laser ablation for the loading of radiofrequency (RF) ion traps is investigated using a nitrogen laser with a maximum pulse energy of 0.17 mJ and a peak intensity of about 250 MW/cm^2. A time-of-flight mass spectrometer is used to measure the ion yield and the distribution of the charge states. Singly charged ions of elements that are presently considered for the use in optical clocks or quantum logic applications could be produced from metallic samples at a rate of the order of magnitude 10^5 ions per pulse. A linear Paul trap was loaded with Th+ ions produced by laser ablation. An overall ion production and trapping efficiency of 10^-7 to 10^-6 was attained. For ions injected individually, a dependence of the capture probability on the phase of the RF field has been predicted. In the experiment this was not observed, presumably because of collective effects within the ablation plume.Comment: submitted to Appl. Phys. B., special issue on ion trappin

Coherent States Measurement Entropy

Coherent states (CS) quantum entropy can be split into two components. The dynamical entropy is linked with the dynamical properties of a quantum system. The measurement entropy, which tends to zero in the semiclassical limit, describes the unpredictability induced by the process of a quantum approximate measurement. We study the CS--measurement entropy for spin coherent states defined on the sphere discussing different methods dealing with the time limit $n \to \infty$. In particular we propose an effective technique of computing the entropy by iterated function systems. The dependence of CS--measurement entropy on the character of the partition of the phase space is analysed.Comment: revtex, 22 pages, 14 figures available upon request (e-mail: [email protected]). Submitted to J.Phys.

Isoperimetry and stability of hyperplanes for product probability measures

International audienceWe investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results can be applied, with a particular emphasis on the logistic measure

Structure determination of neutral mgo clusters-hexagonal nanotubes and cages

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Structure determination of neutral MgO clusters-hexagonal nanotubes and cages

Structural information for neutral magnesium oxide clusters has been obtained by a comparison of their experimental vibrational spectra with predictions from theory. (MgO)n clusters with n = 3-16 have been studied in the gas phase with a tunable IR-UV two-color ionization scheme and size-selective infrared spectra have been measured. These IR spectra are compared to the calculated spectra of the global minimum structures predicted by a hybrid ab initio genetic algorithm. The comparison shows clear evidence that clusters of the composition (MgO)3k (k = 1-5) form hexagonal tubes{,} which confirm previous theoretical predictions. For the intermediate sizes (n [not equal] 3k) cage-like structures containing hexagonal (MgO)3 rings are identified. Except for the cubic (MgO)4 no evidence for bulk like structures is found

Intermolecular interactions of the extended recognition site of VIM-2 metallo-β-lactamase with 1,2,4-triazole-3-thione inhibitors. Validations of a polarizable molecular mechanics potential by ab initio QC

Molecular dynamics on the complexes of inhibitors with Zn-metalloproteins are a privileged area of applications of polarizable molecular mechanics potentials. With which accuracy could these reproduce the QC intermolecular interaction energies in the two mono-zinc cores and in the dizinc core, toward full-fledged MD simulations on the entire protein complexes? We considered the complexes of the extended recognition site of a Zn-dependent metallo-β-lactamase, VIM-2, produced by bacteria responsible for nosocomial infections, with five newly synthesized inhibitors sharing an original dizinc binding group, 1,2,4-triazole-3-thione (TZT). We considered the energy-minimized structures of each of the five VIM-2 complexes obtained with the SIBFA potential. Energy decomposition analyses (EDA) at the HF level enabled to compare the QC and the SIBFA ΔE values and their contributions in the zinc cores, with and without TZT, totaling 30 complexes. With one exception, the ΔE(QC) values were reproduced with relative errors &lt;1.5%. We next considered the complex of the entire inhibitors with an extended model of VIM-2 recognition site, totaling up to 280 atoms. ΔE(SIBFA) could closely reproduce ΔE(QC). EDA analyses were resumed on the complexes of each inhibitor arm with its interacting VIM-2 residues. As a last step, EDA results at correlated levels were analyzed for the mono- and dizinc sites enabling comparisons with dispersion-augmented ΔE(SIBFA) and correlated multipoles and polarizabilities. Closely reproducing ΔE(QC) and the contrasting trends of its individual contributions should enable for dependable free energy perturbation studies and comparisons to recent experimental ΔG values, limiting as much as possible the reliance on error compensations. © 2020 Wiley Periodicals LLC