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

Zeros of linear combinations of Laguerre polynomials from different sequences

We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely $R_n=L_n^{\alpha}+aL_{n}^{\alpha'}$ and $S_n=L_n^{\alpha}+bL_{n-1}^{\alpha'}$. Proofs and numerical counterexamples are given in situations where the zeros of $R_n$, and $S_n$, respectively, interlace (or do not in general) with the zeros of $L_k^{\alpha}$, $L_k^{\alpha'}$, $k=n$ or $n-1$. The results we prove hold for continuous, as well as integral, shifts of the parameter $\alpha$

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

Solving moment problems by dimensional extension

The first part of this paper is devoted to an analysis of moment problems in R^n with supports contained in a closed set defined by finitely many polynomial inequalities. The second part of the paper uses the representation results of positive functionals on certain spaces of rational functions developed in the first part, for decomposing a polynomial which is positive on such a semi-algebraic set into a canonical sum of squares of rational functions times explicit multipliers.Comment: 21 pages, published version, abstract added in migratio

Aging on the edge of stability in disordered systems

Many complex and disordered systems fail to reach equilibrium after they have been quenched or perturbed. Instead, they sluggishly relax toward equilibrium at an ever-slowing, history-dependent rate, a process termed physical aging. The microscopic processes underlying the dynamic slow-down during aging and the reason for its similar occurrence in different systems remain poorly understood. Here, through experiments in crumpled sheets and simulations of a minimal mechanical model - a disordered network of bi-stable elastic elements - we reveal the structural mechanism underlying logarithmic aging in this system. We show that under load, the system self-organizes to a metastable state poised on the verge of an instability, where it can remain for long, but finite times. The system's relaxation is intermittent, advancing via rapid sequences of instabilities, grouped into self-similar, aging avalanches. Crucially, the quiescent dwell times between avalanches grow in proportion to the system's age, due to a slow increase of the lowest effective energy barrier. This slow-down leads to an overall logarithmic aging process.Comment: 7 pages, 3 figure

Tension-controlled switch between collective actuations in active solids

The recent finding of collective actuation in active solids, namely solids embedded with active units, opens the path towards multifunctional materials with genuine autonomy. In such systems, collective dynamics emerge spontaneously and little is known about the way to control or drive them. Here, we combine the experimental study of centimetric model active solids, the numerical study of an agent based model and theoretical arguments to reveal how mechanical tension can serve as a general mechanism for switching between different collective actuation regimes in active solids. We further show the existence of a hysteresis when varying back and forth mechanical tension, highlighting the non-trivial selectivity of collective actuations.Comment: 5 pages, 4 figure

Nonrelativistic Particle in Free Random Gauge Background

The problem of a nonrelativistic particle with an internal color degree of freedom, with and without spin, moving in a free random gauge background is discussed. Freeness is a concept developed recently in the mathematical literature connected with noncommuting random variables. In the context of large-N hermitian matrices, it means that the the multi-matrix model considered contains no bias with respect to the relative orientations of the matrices. In such a gauge background, the spectrum of a colored particle can be solved for analytically. In three dimensions, near zero momentum, the energy distribution for the spinless particle displays a gap, while the energy distribution for the particle with spin does not.Comment: 20 pages, 6 figure

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