Perturbation treatment of symmetry breaking within random matrix theory

We discuss the applicability, within the random matrix theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both two-fold and three-fold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequencies is considered to be missing in the sample. Our findings are relevant for symmetry violation studies in general. (C) 2008 Elsevier B.V. All rights reserved.

Missing levels in acoustic resonators

It is shown that the deviations of the experimental statistics of six chaotic acoustic resonators from Wigner-Dyson random matrix theory predictions are explained by a recent model of random missing levels. In these resonatorsa made of aluminum plates a the larger deviations occur in the spectral rigidity (SRs) while the nearest-neighbor distributions (NNDs) are still close to the Wigner surmise. Good fits to the experimental NNDs and SRs are obtained by adjusting only one parameter, which is the fraction of remaining levels of the complete spectra. For two Sinai stadiums, one Sinai stadium without planar symmetry, two triangles, and a sixth of the three-leaf clover shapes, was found that 7%, 4%, 7%, and 2%, respectively, of eigenfrequencies were not detected.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

Deformations of the Tracy-Widom distribution

In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists of removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristic of extreme values of an uncorrelated sequence, is obtained.

On quantum integrability of the Landau-Lifshitz model

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Multifractality in the random parameter model for multivariate time series

The Random Parameter model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore the scaling properties of the model, as observed in the multifractal structure of the simulated time series. We use the Wavelet Transform Modulus Maxima technique to obtain the multifractal spectrum dependence with the parameters of the model. The model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values. (C) 2009 Elsevier B.V. All rights reserved.

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E(N+1) - E(n))t). The gap E(N+1) - E(n) can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m(b) in HQET.

Quantum statistical correlations in thermal field theories: Boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field phi(c), and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schrodinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field phi(c), a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.

Experimental results on the nonlinear H(infinity) control via quasi-LPV representation and game theory for wheeled mobile robots

In this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear H(infinity) approaches. Two nonlinear H(infinity) controllers that guarantee induced L(2)-norm, between input (disturbances) and output signals, bounded by an attenuation level gamma, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.

An Array Recursive Least-Squares Algorithm With Generic Nonfading Regularization Matrix

We present a novel array RLS algorithm with forgetting factor that circumvents the problem of fading regularization, inherent to the standard exponentially-weighted RLS, by allowing for time-varying regularization matrices with generic structure. Simulations in finite precision show the algorithm`s superiority as compared to alternative algorithms in the context of adaptive beamforming.

Fast Transforms for Acoustic Imaging-Part I: Theory

The classical approach for acoustic imaging consists of beamforming, and produces the source distribution of interest convolved with the array point spread function. This convolution smears the image of interest, significantly reducing its effective resolution. Deconvolution methods have been proposed to enhance acoustic images and have produced significant improvements. Other proposals involve covariance fitting techniques, which avoid deconvolution altogether. However, in their traditional presentation, these enhanced reconstruction methods have very high computational costs, mostly because they have no means of efficiently transforming back and forth between a hypothetical image and the measured data. In this paper, we propose the Kronecker Array Transform ( KAT), a fast separable transform for array imaging applications. Under the assumption of a separable array, it enables the acceleration of imaging techniques by several orders of magnitude with respect to the fastest previously available methods, and enables the use of state-of-the-art regularized least-squares solvers. Using the KAT, one can reconstruct images with higher resolutions than was previously possible and use more accurate reconstruction techniques, opening new and exciting possibilities for acoustic imaging.

The game to play: expanding the co-opetition proposal through the strategic games matrix

Purpose - Using Brandenburger and Nalebuff`s 1995 co-opetition model as a reference, the purpose of this paper is to seek to develop a tool that, based on the tenets of classical game theory, would enable scholars and managers to identify which games may be played in response to the different conflict of interest situations faced by companies in their business environments. Design/methodology/approach - The literature on game theory and business strategy are reviewed and a conceptual model, the strategic games matrix (SGM), is developed. Two novel games are described and modeled. Findings - The co-opetition model is not sufficient to realistically represent most of the conflict of interest situations faced by companies. It seeks to address this problem through development of the SGM, which expands upon Brandenburger and Nalebuff`s model by providing a broader perspective, through incorporation of an additional dimension (power ratio between players) and three novel, respectively, (rival, individualistic, and associative). Practical implications - This proposed model, based on the concepts of game theory, should be used to train decision- and policy-makers to better understand, interpret and formulate conflict management strategies. Originality/value - A practical and original tool to use game models in conflict of interest situations is generated. Basic classical games, such as Nash, Stackelberg, Pareto, and Minimax, are mapped on the SGM to suggest in which situations they Could be useful. Two innovative games are described to fit four different types of conflict situations that so far have no corresponding game in the literature. A test application of the SGM to a classic Intel Corporation strategic management case, in the complex personal computer industry, shows that the proposed method is able to describe, to interpret, to analyze, and to prescribe optimal competitive and/or cooperative strategies for each conflict of interest situation.

On S-matrix factorization of the Landau-Lifshitz model

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schrdinger model [1, 2], that the three-particle S-matrix is factorizable in the first non-trivial order.

Influence of pH on the incorporation and growth of Pb(2)CrO(5) crystallites in silica matrix

Pb(2)CrO(5) nanoparticles were embedded in an amorphous SiO(2) matrix by the sol-gel process. The pH and heat treatment effects were evaluated in terms of structural, microstructural and optical properties from Pb(2)CrO(5)/SiO(2) compounds. X-ray diffraction (XRD), high resolution transmission electron microscopy (HR-TEM), energy dispersive spectroscopy (EDS), and diffuse reflectance techniques were employed. Kubelka-Munk theory was used to calculate diffuse reflectance spectra that were compared to the experimental results. Finally, colorimetric coordinates of the Pb(2)CrO(5)/SiO(2) compounds were shown and discussed. In general, an acid pH initially dissolves Pb(2)CrO(5) nanoparticles and following heat treatment at 600 A degrees C crystallized into PbCrO(4) composition with grain size around 6 nm in SiO(2) matrix. No Pb(2)CrO(5) solubilization was observed for basic pH. These nanoparticles were incorporated in silica matrix showing a variety of color ranging from yellow to orange.

Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.