Random matrices, non-backtracking walks, and orthogonal polynomials

Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the limiting spectral measure play a role in this approach.Comment: (more) minor change

Physics issues in simulations with dynamical overlap fermions

We discuss the impact of various improvements on simulations of dynamical overlap fermions using the Hybrid Monte Carlo algorithm. We focus on the usage of fat links and multiple pseudo-fermion fields.Comment: 14 pages, 10 figure

Polarization effects in the reaction e++e−→ρ++ρ−e^++e^-\to \rho^+ +\rho^- and determination of the ρ−\rho - meson form factors in the time--like region

The electron positron annihilation reaction into four pion production has been studied, through the channel $e^++e^-\to \bar \rho+\rho$. The differential (and total) cross sections and various polarization observables for this reaction have been calculated in terms of the electromagnetic form factors of the corresponding $\gamma^*\rho\rho$ current. The elements of the spin--density matrix of the $\rho -$meson were also calculated. Numerical estimations have been done, with the help of phenomenological form factors obtained in the space--like region of the momentum transfer squared and analytically extended to the time-like region.Comment: 19 pages, 2 figures, to appear in Phys Rev

Search for evidence of two photon contribution in elastic electron proton data

We reanalyze the most recent data on elastic electron proton scattering. We look for a deviation from linearity of the Rosenbluth fit to the differential cross section, which would be the signature of the presence of two photon exchange. The two photon contribution is parametrized by a one parameter formula, based on symmetry arguments. The present data do not show evidence for such deviation.Comment: 15 pages 3 figures More details on the fitting procedure, more explicit explanation

Strongly coupled large-angle stimulated Raman scattering of short laser pulses in plasma-filled capillaries

Strongly coupled large-angle stimulated Raman scattering (LA SRS) of a short intense laser pulse proceeds in a plane plasma-filled capillary differently than in a plasma with open boundaries. Oblique mirror reflections off capillary walls partly suppress the lateral convection of scattered radiation and increase the growth rate of the instability: the convective gain of the LA SRS falls with an angle much slower than in an unbounded plasma and even for the near-forward SRS can be close to that of the direct backscatter. The long-term evolution of LA SRS in the interior of the capillary is dominated by quasi-one-dimensional leaky modes, whose damping is related to the transmission of electromagnetic waves through capillary walls.Comment: 11 pages, 6 figures; to be submitted to Physics of Plasma

Analysis of polarization observables and radiative effects for the reaction pˉ+p→e++e−\bar p+p\rightarrow e^++e^-

The expressions for the differential cross section and of the polarization observables for the reaction $\bar p+p\rightarrow e^++e^-$ are given in terms of the nucleon electromagnetic form factors in the laboratory system. Radiative corrections due to the emission of virtual and real soft photons from the leptons are also calculated. Unlike the center-of- mass system case, they depend on the scattering angle. Polarization effects are derived in the case when the antiproton beam, the target and the electron in the final state are polarized. Numerical estimations have been done for all observables for the PANDA experimental conditions using models for the nucleon electromagnetic form factors in the time-like region. The radiative corrections to the differential cross section are calculated as function of the beam energy and of the electron angle.Comment: 18 pages, 8 figure

On the efficiency of Hamiltonian-based quantum computation for low-rank matrices

We present an extension of Adiabatic Quantum Computing (AQC) algorithm for the unstructured search to the case when the number of marked items is unknown. The algorithm maintains the optimal Grover speedup and includes a small counting subroutine. Our other results include a lower bound on the amount of time needed to perform a general Hamiltonian-based quantum search, a lower bound on the evolution time needed to perform a search that is valid in the presence of control error and a generic upper bound on the minimum eigenvalue gap for evolutions. In particular, we demonstrate that quantum speedup for the unstructured search using AQC type algorithms may only be achieved under very rigid control precision requirements.Comment: 17 pages, no figures, to appear in JM

Limiting Laws of Linear Eigenvalue Statistics for Unitary Invariant Matrix Models

We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test function of statistics is smooth enough and using the asymptotic formulas by Deift et al for orthogonal polynomials with varying weights, we show first that if the support of the Density of States of the model consists of two or more intervals, then in the global regime the variance of statistics is a quasiperiodic function of n generically in the potential, determining the model. We show next that the exponent of the Laplace transform of the probability law is not in general 1/2variance, as it should be if the Central Limit Theorem would be valid, and we find the asymptotic form of the Laplace transform of the probability law in certain cases

Radiative double electron capture by bare nucleus with emission of one photon

Calculation of the cross-section for the process of double electron capture by bare nucleus with emission of a single photon is presented. The double electron capture is evaluated within the framework of Quantum Electrodynamics (QED). Line-Profile Approach (LPA) is employed. Since the radiative double electron capture is governed by the electron correlation, corrections to the interelectron interaction were calculated with high accuracy, partly to all orders of the perturbation theory