Moments of the characteristic polynomial in the three ensembles of random matrices

Moments of the characteristic polynomial of a random matrix taken from any of the three ensembles, orthogonal, unitary or symplectic, are given either as a determinant or a pfaffian or as a sum of determinants. For gaussian ensembles comparing the two expressions of the same moment one gets two remarkable identities, one between an $n\times n$ determinant and an $m\times m$ determinant and another between the pfaffian of a $2n\times 2n$ anti-symmetric matrix and a sum of $m\times m$ determinants.Comment: tex, 1 file, 15 pages [SPhT-T01/016], published J. Phys. A: Math. Gen. 34 (2001) 1-1

Self-vacancies in Gallium Arsenide: an ab initio calculation

We report here a reexamination of the static properties of vacancies in GaAs by means of first-principles density-functional calculations using localized basis sets. Our calculated formation energies yields results that are in good agreement with recent experimental and {\it ab-initio} calculation and provide a complete description of the relaxation geometry and energetic for various charge state of vacancies from both sublattices. Gallium vacancies are stable in the 0, -, -2, -3 charge state, but V_Ga^-3 remains the dominant charge state for intrinsic and n-type GaAs, confirming results from positron annihilation. Interestingly, Arsenic vacancies show two successive negative-U transitions making only +1, -1 and -3 charge states stable, while the intermediate defects are metastable. The second transition (-/-3) brings a resonant bond relaxation for V_As^-3 similar to the one identified for silicon and GaAs divacancies.Comment: 14 page

Effect of iron content and potassium substitution in A0.8_{0.8}Fe1.6_{1.6}Se2_2 (A = K, Rb, Tl) superconductors: a Raman-scattering investigation

We have performed Raman-scattering measurements on high-quality single crystals of the superconductors K$_{0.8}$Fe$_{1.6}$Se$_2$ ($T_c$ = 32 K), Tl$_{0.5}$K$_{0.3}$Fe$_{1.6}$Se$_2$ ($T_c$ = 29 K), and Tl$_{0.5}$Rb$_{0.3}$Fe$_{1.6}$Se$_2$ ($T_c$ = 31 K), as well as of the insulating compound KFe$_{1.5}$Se$_2$. To interpret our results, we have made first-principles calculations for the phonon modes in the ordered iron-vacancy structure of K$_{0.8}$Fe$_{1.6}$Se$_2$. The modes we observe can be assigned very well from our symmetry analysis and calculations, allowing us to compare Raman-active phonons in the AFeSe compounds. We find a clear frequency difference in most phonon modes between the superconducting and non-superconducting potassium crystals, indicating the fundamental influence of iron content. By contrast, substitution of K by Tl or Rb in A$_{0.8}$Fe$_{1.6}$Se$_2$ causes no substantial frequency shift for any modes above 60 cm$^{-1}$, demonstrating that the alkali-type metal has little effect on the microstructure of the FeSe layer. Several additional modes appear below 60 cm$^{-1}$ in Tl- and Rb-substituted samples, which are vibrations of heavier Tl and Rb ions. Finally, our calculations reveal the presence of "chiral" phonon modes, whose origin lies in the chiral nature of the K$_{0.8}$Fe$_{1.6}$Se$_2$ structure.Comment: 11 pages, 10 figures and 2 table

On possible superconductivity in the doped ladder compound La_(1-x)Sr_xCuO_2.5

LaCuO_2.5 is a system of coupled, two-chain, cuprate ladders which may be doped systematically by Sr substitution. Motivated by the recent synthesis of single crystals, we investigate theoretically the possibility of superconductivity in this compound. We use a model of spin fluctuation-mediated superconductivity, where the pairing potential is strongly peaked at \pi in the ladder direction. We solve the coupled gap equations on the bonding and antibonding ladder bands to find superconducting solutions across the range of doping, and discuss their relevance to the real material.Comment: RevTex, 4 pages, 7 figure

Remarks on the Collective Quantization of the SU(2) Skyrme Model

We point out the question of ordering momentum operator in the canonical \break quantization of the SU(2) Skyrme Model. Thus, we suggest a new definition for the momentum operator that may solve the infrared problem that appears when we try to minimize the Quantum Hamiltonian.Comment: 8 pages, plain tex, IF/UFRJ/9

Activated sampling in complex materials at finite temperature: the properly-obeying-probability activation-relaxation technique

While the dynamics of many complex systems is dominated by activated events, there are very few simulation methods that take advantage of this fact. Most of these procedures are restricted to relatively simple systems or, as with the activation-relaxation technique (ART), sample the conformation space efficiently at the cost of a correct thermodynamical description. We present here an extension of ART, the properly-obeying-probability ART (POP-ART), that obeys detailed balance and samples correctly the thermodynamic ensemble. Testing POP-ART on two model systems, a vacancy and an interstitial in crystalline silicon, we show that this method recovers the proper thermodynamical weights associated with the various accessible states and is significantly faster than MD in the diffusion of a vacancy below 700 K.Comment: 10 pages, 3 figure

Calculation of some determinants using the s-shifted factorial

Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer's symbol) and the falling factorial. It is a special case of polynomial sequence of the binomial type studied in combinatorics theory. In terms of the gamma function, an extension is defined for negative integers and even complex values. Properties, mainly composition laws and binomial formulae, are given. They are used to evaluate families of generalized Vandermonde determinants with s-shifted factorials as elements, instead of power functions.Comment: 25 pages; added section 5 for some examples of application

The Effects of Negative Legacies on the Adjustment of Parentally Bereaved Children and Adolescents

This is a report of a qualitative analysis of a sample of bereaved families in which one parent died and in which children scored in the clinical range on the Child Behavior Check List. The purpose of this analysis was to learn more about the lives of these children. They were considered to be at risk of developing emotional and behavioral problems associated with the death. We discovered that many of these “high risk” children had a continuing bond with the deceased that was primarily negative and troubling for them in contrast to a comparison group of children not at risk from the same study. Five types of legacies, not mutually exclusive, were identified: health related, role related, personal qualities, legacy of blame, and an emotional legacy. Coping behavior on the part of the surviving parent seemed to make a difference in whether or not a legacy was experienced as negative