Random matrix models with log-singular level confinement: method of fictitious fermions

Joint distribution function of N eigenvalues of U(N) invariant random-matrix ensemble can be interpreted as a probability density to find N fictitious non-interacting fermions to be confined in a one-dimensional space. Within this picture a general formalism is developed to study the eigenvalue correlations in non-Gaussian ensembles of large random matrices possessing non-monotonic, log-singular level confinement. An effective one-particle Schroedinger equation for wave-functions of fictitious fermions is derived. It is shown that eigenvalue correlations are completely determined by the Dyson's density of states and by the parameter of the logarithmic singularity. Closed analytical expressions for the two-point kernel in the origin, bulk, and soft-edge scaling limits are deduced in a unified way, and novel universal correlations are predicted near the end point of the single spectrum support.Comment: 13 pages (latex), Presented at the MINERVA Workshop on Mesoscopics, Fractals and Neural Networks, Eilat, Israel, March 199

Cefazolin Prophylaxis for Total Joint Arthroplasty: Obese Patients Are Frequently Underdosed and at Increased Risk of Periprosthetic Joint Infection

Background One of the most effective prophylactic strategies against periprosthetic joint infection (PJI) is administration of perioperative antibiotics. Many orthopedic surgeons are unaware of the weight-based dosing protocol for cefazolin. This study aimed at elucidating what proportion of patients receiving cefazolin prophylaxis are underdosed and whether this increases the risk of PJI. Methods A retrospective study of 17,393 primary total joint arthroplasties receiving cefazolin as perioperative prophylaxis from 2005 to 2017 was performed. Patients were stratified into 2 groups (underdosed and adequately dosed) based on patient weight and antibiotic dosage. Patients who developed PJI within 1 year following index procedure were identified. A bivariate and multiple logistic regression analyses were performed to control for potential confounders and identify risk factors for PJI. Results The majority of patients weighing greater than 120 kg (95.9%, 944/984) were underdosed. Underdosed patients had a higher rate of PJI at 1 year compared with adequately dosed patients (1.51% vs 0.86%, P = .002). Patients weighing greater than 120 kg had higher 1-year PJI rate than patients weighing less than 120 kg (3.25% vs 0.83%, P < .001). Patients who were underdosed (odds ratio, 1.665; P = .006) with greater comorbidities (odds ratio, 1.259; P < .001) were more likely to develop PJI at 1 year. Conclusion Cefazolin underdosing is common, especially for patients weighing more than 120 kg. Our study reports that underdosed patients were more likely to develop PJI. Orthopedic surgeons should pay attention to the weight-based dosing of antibiotics in the perioperative period to avoid increasing risk of PJI

Entanglement and nonclassicality for multi-mode radiation field states

Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multi-mode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beamsplitters, in a transparent manner. For single mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beamsplitter, these conditions turn exactly into signatures of NPT entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two--mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beamsplitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three--mode beamsplitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.Comment: Latex, 46 page

Maximum entropy and the problem of moments: A stable algorithm

We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an optimal solution can be constructed iteratively. We demonstrate the performance and stability of our algorithm with several tests on numerically difficult functions. We then consider an electronic structure application, the electronic density of states of amorphous silica and study the convergence of Fermi level with increasing number of moments.Comment: 4 pages including 3 figure

Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz

We apply the maximum entropy principle to construct the natural invariant density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique that is based on the solution of Hausdorff moment problem via maximizing Shannon entropy, we estimate the invariant density and the Lyapunov exponent of nonlinear maps in one-dimension from a knowledge of finite number of moments. The accuracy and the stability of the algorithm are illustrated by comparing our results to a number of nonlinear maps for which the exact analytical results are available. Furthermore, we also consider a very complex example for which no exact analytical result for invariant density is available. A comparison of our results to those available in the literature is also discussed.Comment: 16 pages including 6 figure

Coherent states of a charged particle in a uniform magnetic field

The coherent states are constructed for a charged particle in a uniform magnetic field based on coherent states for the circular motion which have recently been introduced by the authors.Comment: 2 eps figure

Two-band random matrices

Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of spectra are directly reconstructed from the recurrence equation for orthogonal polynomials associated with a given random matrix ensemble. It is established that an eigenvalue gap does not affect the local eigenvalue correlations which follow the universal sine and the universal multicritical laws in the bulk and soft-edge scaling limits, respectively. By contrast, global smoothed eigenvalue correlations do reflect the presence of a gap, and are shown to satisfy a new universal law exhibiting a sharp dependence on the odd/even dimension of random matrices whose spectra are bounded. In the case of unbounded spectrum, the corresponding universal `density-density' correlator is conjectured to be generic for chaotic systems with a forbidden gap and broken time reversal symmetry.Comment: 12 pages (latex), references added, discussion enlarge

Total Widths And Slopes From Complex Regge Trajectories

Maximally complex Regge trajectories are introduced for which both Re $\alpha(s)$ and Im $\alpha(s)$ grow as $s^{1-\epsilon}$ ($\epsilon$ small and positive). Our expression reduces to the standard real linear form as the imaginary part (proportional to $\epsilon$) goes to zero. A scaling formula for the total widths emerges: $\Gamma_{TOT}/M\to$ constant for large M, in very good agreement with data for mesons and baryons. The unitarity corrections also enhance the space-like slopes from their time-like values, thereby resolving an old problem with the $\rho$ trajectory in $\pi N$ charge exchange. Finally, the unitarily enhanced intercept, $\alpha_{\rho}\approx 0.525$, \nolinebreak is in good accord with the Donnachie-Landshoff total cross section analysis.Comment: 9 pages, 3 Figure

Vector Continued Fractions using a Generalised Inverse

A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse permits construction of vector analogues of the Jacobi continued fraction. These vector Jacobi fractions are related to vector and scalar-valued polynomial functions of the vectors, which satisfy recurrence relations similar to those of orthogonal polynomials. The vector Jacobi fraction has strong convergence properties which are demonstrated analytically, and illustrated numerically.Comment: Published form - minor change

Function reconstruction as a classical moment problem: A maximum entropy approach

We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we reconstruct a set of functions using an iterative entropy optimization scheme, and study the convergence profile as the number of moments is increased. We consider a wide variety of functions that include a distribution with a sharp discontinuity, a rapidly oscillatory function, a distribution with singularities, and finally a distribution with several spikes and fine structure. The last example is important in the context of the determination of the natural density of the logistic map. The convergence of the method is studied by comparing the moments of the approximated functions with the exact ones. Furthermore, by varying the number of moments and iterations, we examine to what extent the features of the functions, such as the divergence behavior at singular points within the interval, is reproduced. The proximity of the reconstructed maximum entropy solution to the exact solution is examined via Kullback-Leibler divergence and variation measures for different number of moments.Comment: 20 pages, 17 figure