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

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

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

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

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

SsODNet: The Solar system Open Database Network

The sample of Solar system objects has dramatically increased over the last decade. The amount of measured properties (e.g., diameter, taxonomy, rotation period, thermal inertia) has grown even faster. However, this wealth of information is spread over a myriad of articles, under many different designations per object. We provide a solution to the identification of Solar system objects from any of their multiple names or designations. We also compile and rationalize their properties to provide an easy access to them. We aim to continuously update the database as new measurements become available. We built a Web Service, SsODNet, that offers four access points, each corresponding to an identified necessity in the community: name resolution (quaero), compilation of a large corpus of properties (datacloud), determination of the best estimate among compiled values (ssoCard), and statistical description of the population (ssoBFT). The SsODNet interfaces are fully operational and freely accessible to everyone. The name resolver quaero translates any of the ~5.3 million designations of objects into their current official designation. The datacloud compiles about 105 million parameters (osculating and proper elements, pair and family membership, diameter, albedo, mass, density, rotation period, spin coordinates, phase function parameters, colors, taxonomy, thermal inertia, and Yarkovsky drift) from over 3,000 articles (and growing). For each of the known asteroids and dwarf planets (~1.2 million), a ssoCard providing a single best-estimate for each parameter is available. The SsODNet service provides these resources in a fraction of second upon query. Finally, the large ssoBFT table compiles all the best-estimates in a single table for population-wide studies

Boundary conditions associated with the Painlev\'e III' and V evaluations of some random matrix averages

In a previous work a random matrix average for the Laguerre unitary ensemble, generalising the generating function for the probability that an interval $(0,s)$ at the hard edge contains $k$ eigenvalues, was evaluated in terms of a Painlev\'e V transcendent in $\sigma$-form. However the boundary conditions for the corresponding differential equation were not specified for the full parameter space. Here this task is accomplished in general, and the obtained functional form is compared against the most general small $s$ behaviour of the Painlev\'e V equation in $\sigma$-form known from the work of Jimbo. An analogous study is carried out for the the hard edge scaling limit of the random matrix average, which we have previously evaluated in terms of a Painlev\'e \IIId transcendent in $\sigma$-form. An application of the latter result is given to the rapid evaluation of a Hankel determinant appearing in a recent work of Conrey, Rubinstein and Snaith relating to the derivative of the Riemann zeta function

Block orthogonal polynomials: I. Definition and properties

Constrained orthogonal polynomials have been recently introduced in the study of the Hohenberg-Kohn functional to provide basis functions satisfying particle number conservation for an expansion of the particle density. More generally, we define block orthogonal (BO) polynomials which are orthogonal, with respect to a first Euclidean scalar product, to a given $i$-dimensional subspace ${\cal E}_i$ of polynomials associated with the constraints. In addition, they are mutually orthogonal with respect to a second Euclidean scalar product. We recast the determination of these polynomials into a general problem of finding particular orthogonal bases in an Euclidean vector space endowed with distinct scalar products. An explicit two step Gram-Schmidt orthogonalization (G-SO) procedure to determine these bases is given. By definition, the standard block orthogonal (SBO) polynomials are associated with a choice of ${\cal E}_i$ equal to the subspace of polynomials of degree less than $i$. We investigate their properties, emphasizing similarities to and differences from the standard orthogonal polynomials. Applications to classical orthogonal polynomials will be given in forthcoming papers.Comment: This is a reduced version of the initial manuscript, the number of pages being reduced from 34 to 2

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