From Random Matrices to Stochastic Operators

We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local eigenvalue behavior. The stochastic Airy operator displays soft edge behavior, associated with the Airy kernel. The stochastic Bessel operator displays hard edge behavior, associated with the Bessel kernel. The article concludes with suggestions for a stochastic sine operator, which would display bulk behavior, associated with the sine kernel.Comment: 41 pages, 5 figures. Submitted to Journal of Statistical Physics. Changes in this revision: recomputed Monte Carlo simulations, added reference [19], fit into margins, performed minor editin

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

Rovibrationally resolved photodissociation of HeH+

Accurate photodissociation cross sections have been obtained for the A-X electronic transition of HeH+ using ab initio potential curves and dipole transition moments. Partial cross sections have been evaluated for all rotational transitions from the vibrational levels v"=0-11 and over the entire accessible wavelength range 100-1129 Angstrom. Assuming a Boltzmann distribution of the rovibrational levels of the X state, photodissociation cross sections are presented for temperatures between 500 and 12,000 K. A similar set of calculations was performed for the pure rovibrational photodissociation in the X-X electronic ground state, but covering photon wavelengths into the far infrared. Applications of the cross sections to the destruction of HeH+in the early Universe and in UV-irradiated environments such as primordial halos and protoplanetary disks are briefly discussed

Mice lacking C1q or C3 show accelerated rejection of minor H disparate skin grafts and resistance to induction of tolerance

Complement activation is known to have deleterious effects on organ transplantation. On the other hand, the complement system is also known to have an important role in regulating immune responses. The balance between these two opposing effects is critical in the context of transplantation. Here, we report that female mice deficient in C1q (C1qa(−/−)) or C3 (C3(−/−)) reject male syngeneic grafts (HY incompatible) at an accelerated rate compared with WT mice. Intranasal HY peptide administration, which induces tolerance to syngeneic male grafts in WT mice, fails to induce tolerance in C1qa(−/−) or C3(−/−) mice. The rejection of the male grafts correlated with the presence of HY D(b)Uty-specific CD8(+) T cells. Consistent with this, peptide-treated C1qa(−/−) and C3(−/−) female mice rejecting male grafts exhibited more antigen-specific CD8(+)IFN-γ(+) and CD8(+)IL-10(+) cells compared with WT females. This suggests that accumulation of IFN-γ- and IL-10-producing T cells may play a key role in mediating the ongoing inflammatory process and graft rejection. Interestingly, within the tolerized male skin grafts of peptide-treated WT mice, IFN-γ, C1q and C3 mRNA levels were higher compared to control female grafts. These results suggest that C1q and C3 facilitate the induction of intranasal tolerance

Decomposition of fractional quantum Hall states: New symmetries and approximations

We provide a detailed description of a new symmetry structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall states first obtained in Ref. 1, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can be obtained without exact diagonalization through a differential equation method that we conjecture to be generic to other FQH model states. The symmetry rules in Ref. 1 as well as the ones we obtain for the spin singlet states allow us to build approximations of FQH states that exhibit increasing overlap with the exact state (as a function of system size). We show that these overlaps reach unity in the thermodynamic limit even though our approximation omits more than half of the Hilbert space. We show that the product rule is valid for any FQH state which can be written as an expectation value of parafermionic operators.Comment: 22 pages, 8 figure

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

Fragmentation Properties of Three-membered Ring Heterocyclic Molecules by Partial Ion Yield Spectroscopy: C2H4O and C2H4S

We investigated the photofragmentation properties of two three-membered ring heterocyclic molecules, C2H4O and C2H4S, by total and partial ion yield spectroscopy. Positive and negative ions have been collected as a function of photon energy around the C 1s and O 1s ionization thresholds in C2H4O, and around the S 2p and C 1s thresholds in C2H4S. We underline similarities and differences between these two analogous systems. We present a new assignment of the spectral features around the C K-edge and the sulfur L2,3 edges in C2H4S. In both systems, we observe high fragmentation efficiency leading to positive and negative ions when exciting these molecules at resonances involving core-to-Rydberg transitions. The system, with one electron in an orbital far from the ionic core, relaxes preferentially by spectator Auger decay, and the resulting singly charged ion with two valence holes and one electron in an outer diffuse orbital can remain in excited states more susceptible to dissociation. A state-selective fragmentation pattern is analyzed in C2H4S which leads to direct production of S2+ following the decay of virtual-orbital excitations to final states above the double-ionization threshold

On Poincare and logarithmic Sobolev inequalities for a class of singular Gibbs measures

This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular pair interaction. The functional inequalities come from convexity. We prove and characterize optimality in the case of quadratic confinement via a factorization of the measure. This optimality phenomenon holds for all beta Hermite ensembles including the Gaussian unitary ensemble, a famous exactly solvable model of random matrix theory. We further explore exact solvability by reviewing the relation to Dyson-Ornstein-Uhlenbeck diffusion dynamics admitting the Hermite-Lassalle orthogonal polynomials as a complete set of eigenfunctions. We also discuss the consequence of the log-Sobolev inequality in terms of concentration of measure for Lipschitz functions such as maxima and linear statistics.Comment: Minor improvements. To appear in Geometric Aspects of Functional Analysis -- Israel Seminar (GAFA) 2017-2019", Lecture Notes in Mathematics 225

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.