The ensemble of random Markov matrices

The ensemble of random Markov matrices is introduced as a set of Markov or stochastic matrices with the maximal Shannon entropy. The statistical properties of the stationary distribution pi, the average entropy growth rate $h$ and the second largest eigenvalue nu across the ensemble are studied. It is shown and heuristically proven that the entropy growth-rate and second largest eigenvalue of Markov matrices scale in average with dimension of matrices d as h ~ log(O(d)) and nu ~ d^(-1/2), respectively, yielding the asymptotic relation h tau_c ~ 1/2 between entropy h and correlation decay time tau_c = -1/log|nu| . Additionally, the correlation between h and and tau_c is analysed and is decreasing with increasing dimension d.Comment: 12 pages, 6 figur

Vertical Structure of the Outer Accretion Disk in Persistent Low-Mass X-Ray Binaries

We have investigated the influence of X-ray irradiation on the vertical structure of the outer accretion disk in low-mass X-ray binaries by performing a self-consistent calculation of the vertical structure and X-ray radiation transfer in the disk. Penetrating deep into the disk, the field of scattered X-ray photons with energy $E\gtrsim10$\,keV exerts a significant influence on the vertical structure of the accretion disk at a distance $R\gtrsim10^{10}$\,cm from the neutron star. At a distance $R\sim10^{11}$\,cm, where the total surface density in the disk reaches $\Sigma_0\sim20$\,g\,cm$^{-2}$, X-ray heating affects all layers of an optically thick disk. The X-ray heating effect is enhanced significantly in the presence of an extended atmospheric layer with a temperature $T_{atm}\sim(2\div3)\times10^6$\,K above the accretion disk. We have derived simple analytic formulas for the disk heating by scattered X-ray photons using an approximate solution of the transfer equation by the Sobolev method. This approximation has a $\gtrsim10$\,% accuracy in the range of X-ray photon energies $E<20$\,keV.Comment: 19 pages, 8 figures, published in Astronomy Letter

The properties of the three-nucleon system with the dressed-bag model for nn interaction. I: New scalar three-body force

A multi-component formalism is developed to describe three-body systems with nonstatic pairwise interactions and non-nucleonic degrees of freedom. The dressed-bag model for $NN$ interaction based on the formation of an intermediate six-quark bag dressed by a $\sigma$-field is applied to the $3N$ system, where it results in a new three-body force between the six-quark bag and a third nucleon. Concise variational calculations of $3N$ bound states are carried out in the dressed-bag model including the new three-body force. It is shown that this three-body force gives at least half the $3N$ total binding energy, while the weight of non-nucleonic components in the $^3$H and $^3$He wavefunctions can exceed 10%. The new force model provides a very good description of $3N$ bound states with a reasonable magnitude of the $\sigma NN$ coupling constant. The model can serve as a natural bridge between dynamical description of few-nucleon systems and the very successful Walecka approach to heavy nuclei and nuclear matter.Comment: 26 pages, Latex, 7 figure

COMPETITION AMONG HOSPITALS AND ITS MEASUREMENT: THEORY AND A CASE STUDY

Our paper provides several insights on the characteristics of the concept of “Poles d’Excellence Rurale” (PER) through bilateral comparisons with that of Competitive Pole (CP) and cluster. The concept of PER is a French government’ initiative designed for the development of rural areas similar to that of the Competitive Pole. We emphasize important particularities of these concepts by analyzing some of their similarities and major differences.Pole d’Excellence Rurale, Competitive Pole, cluster, rural development

The High-Flux Backscattering Spectrometer at the NIST Center for Neutron Research

We describe the design and current performance of the high-flux backscattering spectrometer located at the NIST Center for Neutron Research. The design incorporates several state-of-the-art neutron optical devices to achieve the highest flux on sample possible while maintaining an energy resolution of less than 1mueV. Foremost among these is a novel phase-space transformation chopper that significantly reduces the mismatch between the beam divergences of the primary and secondary parts of the instrument. This resolves a long-standing problem of backscattering spectrometers, and produces a relative gain in neutron flux of 4.2. A high-speed Doppler-driven monochromator system has been built that is capable of achieving energy transfers of up to +-50mueV, thereby extending the dynamic range of this type of spectrometer by more than a factor of two over that of other reactor-based backscattering instruments

Kondo screening and exhaustion in the periodic Anderson model

We investigate the paramagnetic periodic Anderson model using the dynamical mean-field theory in combination with the modified perturbation theory which interpolates between the weak and strong coupling limits. For the symmetric PAM, the ground state is always a singlet state. However, as function of the hybridization strength, a crossover from collective to local Kondo screening is found. Reducing the number of conduction electrons, the local Kondo singlets remain stable. The unpaired f-electrons dominate the physics of the system. For very low conduction electron densities, a large increase of the effective mass of the quasiparticles is visible, which is interpreted as the approach of the Mott-Hubbard transition.Comment: 10 pages, 8 figures, accepted by Phys. Rev.

Mixing Quantum and Classical Mechanics

Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket is antisymmetric and satisfies the Jacobi identity, and, therefore, leads to a natural description of interaction between quantum and classical degrees of freedom. We apply the formalism to coupled quantum and classical oscillators and show how various approximations, such as the mean-field and the multiconfiguration mean-field approaches, can be obtained from the quantum-classical equation of motion.Comment: 31 pages, LaTeX2

Tunnelling Studies of Two-Dimensional States in Semiconductors with Inverted Band Structure: Spin-orbit Splitting, Resonant Broadening

The results of tunnelling studies of the energy spectrum of two-dimensional (2D) states in a surface quantum well in a semiconductor with inverted band structure are presented. The energy dependence of quasimomentum of the 2D states over a wide energy range is obtained from the analysis of tunnelling conductivity oscillations in a quantizing magnetic field. The spin-orbit splitting of the energy spectrum of 2D states, due to inversion asymmetry of the surface quantum well, and the broadening of 2D states at the energies, when they are in resonance with the heavy hole valence band, are investigated in structures with different strength of the surface quantum well. A quantitative analysis is carried out within the framework of the Kane model of the energy spectrum. The theoretical results are in good agreement with the tunnelling spectroscopy data.Comment: 29 pages, RevTeX, submitted in Phys.Rev.B. Figures available on request from [email protected]

From Regular to Chaotic States in Atomic Nuclei

An interesting aspect of nuclear dynamics is the co--existence, in atomic nuclei, of regular and chaotic states. In the first part of the present work, we review the state of the art of nuclear dynamics and use a schematic shell model to show how a very simple and schematic nucleon--nucleon interaction can produce an order$\to$chaos transition. The second part is devoted to a discussion of the wave function behaviour and decay of chaotic states using some simple models (to be published in Rivista Nuovo Cimento).Comment: 65 pages, LaTex (the figures are not included), Preprint DFPD/94/TH/26, University of Padov

Very High Energy Gamma-Ray Emission from the Blazar Markarian 421

Very high energy gamma-ray emission from the BL Lac object Markarian 421 has been detected over three observing seasons on 59 nights between April 1992 and June 1994 with the Whipple 10-meter imaging Cherenkov telescope. During its initial detection in 1992, its flux above 500 GeV was 1.6$\times$10$^{-11}$photons cm$^{-2}$ s$^{-1}$. Observations in 1993 confirmed this level of emission. For observations made between December 1993 and April 1994, its intensity was a factor of 2.2$\pm$0.5 lower. Observations on 14 and 15 May, 1994 showed an increase over this quiescent level by a factor of $\sim$10 (Kerrick et al. 1995). This strong outburst suggests that 4 episodes of increased flux measurements on similar time scales in 1992 and 1994 may be attributed to somewhat weaker outbursts. The variability of the TeV gamma-ray emission from Markarian 421 stands in contrast to EGRET observations (Lin et al. 1994) which show no evidence for variability.Comment: gzip compressed tar file including LaTeX text and 4 postscript figures (14 pages total incl. 4 tables), accepted for publication in the Astrophysical Journal. Contact address is [email protected]