Inverse participation ratios in the XXZ spin chain

We investigate numerically the inverse participation ratios in a spin-1/2 XXZ chain, computed in the "Ising" basis (i.e., eigenstates of $\sigma^z_i$). We consider in particular a quantity $T$, defined by summing the inverse participation ratios of all the eigenstates in the zero magnetization sector of a finite chain of length $N$, with open boundary conditions. From a dynamical point of view, $T$ is proportional to the stationary return probability to an initial basis state, averaged over all the basis states (initial conditions). We find that $T$ exhibits an exponential growth, $T\sim\exp(aN)$, in the gapped phase of the model and a linear scaling, $T\sim N$, in the gapless phase. These two different behaviors are analyzed in terms of the distribution of the participation ratios of individual eigenstates. We also investigate the effect of next-nearest-neighbor interactions, which break the integrability of the model. Although the massive phase of the non-integrable model also has $T\sim\exp(aN)$, in the gapless phase $T$ appears to saturate to a constant value.Comment: 8 pages, 7 figures. v2: published version (one figure and 3 references added, several minor changes

Shock wave instability and the carbuncle phenomenon: same intrinsic origin ?

The theoretical linear stability of a shock wave moving in an unlimited homogeneous environment has been widely studied during the last fifty years. Important results have been obtained by Dyakov (1954), Landau & Lifchitz (1959) and then by Swan & Fowles (1975) where the fluctuating quantities are written as normal modes. More recently, numerical studies on upwind finite difference schemes have shown some instabilities in the case of the motion of an inviscid perfect gas in a rectangular channel. The purpose of this paper is first to specify a mathematical formulation for the eigenmodes and to exhibit a new mode which was not found by the previous stability analysis of shock waves. Then, this mode is confirmed by numerical simulations which may lead to a new understanding of the so-called carbuncle phenomenon

A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures

in pressInternational audienceIn this paper we make a comparison between the two-scale asymptotic expansion method for periodic homogenization and the so-called Bloch wave method. It is well-known that the homogenized tensor coincides with the Hessian matrix of the first Bloch eigenvalue when the Bloch parameter vanishes. In the context of the two-scale asymptotic expansion method, there is the notion of high order homogenized equation [5] where the homogenized equation can be improved by adding small additional higher order differential terms. The next non-zero high order term is a fourth-order term, accounting for dispersion effects (see e.g. [23], [18], [15]). Surprisingly, this homogenized fourth-order tensor is not equal to the fourth-order tensor arising in the Taylor expansion of the first Bloch eigenvalue, which is often called Burnett tensor. Here, we establish an exact relation between the homogenized fourth-order tensor and the Burnett fourth-order tensor. It was proved in [11] that the Burnett fourth-order tensor has a sign. For the special case of a simple laminate we prove that the homogenized fourth-order tensor may change sign. In the elliptic case we explain the difference between the homogenized and Burnett fourth-order tensors by a difference in the source term which features an additional corrector term. Finally, for the wave equation, the two fourth-order tensors coincide again, so dispersion is unambiguously defined, and only the source terms differ as in the elliptic case

Geometric Interpretation of the Quantum Master Equation in the BRST--anti-BRST Formalism

The geometric interpretation of the antibracket formalism given by Witten is extended to cover the anti-BRST symmetry. This enables one to formulate the quantum master equation for the BRST--anti-BRST formalism in terms of integration theory over a supermanifold. A proof of the equivalence of the standard antibracket formalism with the antibracket formalism for the BRST--anti-BRST symmetry is also given.Comment: 12 page

Use of anticoagulants in elderly patients: practical recommendations

Elderly people represent a patient population at high thromboembolic risk, but also at high hemorrhagic risk. There is a general tendency among physicians to underuse anticoagulants in the elderly, probably both because of underestimation of thromboembolic risk and overestimation of bleeding risk. The main indications for anticoagulation are venous thromboembolism (VTE) prophylaxis in medical and surgical settings, VTE treatment, atrial fibrillation (AF) and valvular heart disease. Available anticoagulants for VTE prophylaxis and initial treatment of VTE are low molecular weight heparins (LMWH), unfractionated heparin (UFH) or synthetic anti-factor Xa pentasaccharide fondaparinux. For long-term anticoagulation vitamin K antagonists (VKA) are the first choice and only available oral anticoagulants nowadays. Assessing the benefit-risk ratio of anticoagulation is one of the most challenging issues in the individual elderly patient, patients at highest hemorrhagic risk often being those who would have the greatest benefit from anticoagulants. Some specific considerations are of utmost importance when using anticoagulants in the elderly to maximize safety of these treatments, including decreased renal function, co-morbidities and risk of falls, altered pharmacodynamics of anticoagulants especially VKAs, association with antiplatelet agents, patient education. Newer anticoagulants that are currently under study could simplify the management and increase the safety of anticoagulation in the future

Lidar-radar velocimetry using a pulse-to-pulse coherent rf-modulated Q-switched laser.

International audienceAn rf-modulated pulse train from a passively Q-switched Nd:YAG laser has been generated using an extra-cavity acousto-optic modulator. The rf modulation reproduces the spectral quality of the local oscillator. It leads to a high pulse-to-pulse phase coherence, i.e., phase memory, over thousands of pulses. The potentialities of this transmitter for lidar-radar are demonstrated by performing Doppler velocimetry on indoor moving targets. The experimental results are in good agreement with a model based on elementary signal processing theory. In particular, we show experimentally and theoretically that lidar-radar is a promising technique that allows discrimination between translation and rotation movements. Being independent of the laser internal dynamics, this scheme can be applied to any Q-switched laser

Characterization of eddy-current testing inverse problems using adaptive databases

International audienceOne of the main challenges in Eddy Current Testing (ECT) is the solution of the inverse problem, i.e., the determination of the defect properties knowing the measured data. To this end, many approaches and mathematical tools have been proposed. The so-called adaptive database-method has recently been developed. Its main idea is to store corresponding input-output data pairs in a database and, by fitting an interpolator to these samples, to solve approximately the forward and inverse problems at a low computational cost

Statistical inference for rough volatility: Central limit theorems

In recent years, there has been substantive empirical evidence that stochastic volatility is rough. In other words, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter $H<0.5$. In this paper, we derive a consistent and asymptotically mixed normal estimator of $H$ based on high-frequency price observations. In contrast to previous works, we work in a semiparametric setting and do not assume any a priori relationship between volatility estimators and true volatility. Furthermore, our estimator attains a rate of convergence that is known to be optimal in a minimax sense in parametric rough volatility models

Thoughts on CCS/U

Expert presentation given in the context of the Expert panel "Future of Gas" led by Deloitte for the SPF Econom