We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced ...to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.
A SYK–like model close to the colored tensor models has recently been proposed 1. Building on results obtained in tensor models 2, we discuss the complete 1/N expansion of the model. We detail the ...two and four point functions at leading order. The leading order two point function is a sum over melonic graphs, and the leading order relevant four point functions are sums over dressed ladder diagrams. We then show that any order in the 1/N series of the two point function can be written solely in term of the leading order two and four point functions. The full 1/N expansion of arbitrary correlations can be obtained by similar methods.
BPS Dendroscopy on Local $$\mathbb {P}^2 Bousseau, Pierrick; Descombes, Pierre; Le Floch, Bruno ...
Communications in mathematical physics,
04/2024, Letnik:
405, Številka:
4
Journal Article
Airplanes are nowadays the main transport solution for travelers and this makes aviation one of the most important and strategic social and economic fields. However, tragedies of airplane incidents ...can happen because of human or technical faults or even bad weather which threatens this field. Furthermore, these aviation incidents are very deadly and the current aviation safety measures and technologies are not enough in order to completely succeed in the rescue of travelers, pilots and cargo of an airplane in free fall in the air. Many inventions are proposed as solutions for the safety of these airplanes but their application is difficult and requires the rebalancing of the aircraft in free fall which is a hard task. This study aims to present a summary of the new invention in aviation which was accepted in the Moroccan Office of Industrial and Commercial Property (OMPIC) in Morocco. This invention enables the rescue in air in case of an accident or failure in an airplane. Current technological advances in fuel propulsion power and material strength make this invention summarized here possible to save hundreds of lives every year. This article explains also a new proposed navigation system based on a second invention filed in the same Moroccan Office of Patents which can be very useful for aircraft and even other vessels like submarines. This navigation system based on principles of the compass is a very cheap computerized analysis and control system which, compared to other declared benchmarks, can make airplanes achieve navigation more independent from terrestrial control stations and satellites and can significantly enhance future autopilot systems. The students and even the experts are therefore invited to understand both these two inventions since the presented methods can be used even in other inventions in different fields regarding moving objects. The specialists in aviation will also find in this article a new opportunity to enhance the safety measures and technologies of this important field of transport.
The Sine-Gordon model is obtained by tilting the law of a log-correlated Gaussian field X defined on a subset of R d by the exponential of its cosine, namely exp(α ∫ cos(βX)). It is an important ...model in quantum field theory or in statistic physics like in the study of log-gases. In spite of its relatively simple definition, the model has a very rich phenomenology. While the integral ∫ cos(βX) can properly be defined when β 2 < d using the standard Wick normalisation of cos(βX), a more involved renormalization procedure is needed when β 2 ∈ d, 2d). In particular it exhibits a countable sequence of phase transition accumulating to the left of β = √ 2d, each transitions corresponding to the addition of an extra term in the renormalization scheme. The final threshold β = √ 2 corresponds to the Kosterlitz-Thouless (KT) phase transition of the log-gas. In this paper, we present a novel probabilistic approach to renormalization of the two-dimensional boundary (or 1-dimensional) Sine-Gordon model up to the KT threshold β = √ 2. The purpose of this approach is to propose a simple and flexible method to treat this problem which, unlike the existing renormalization group techniques, does not rely on translation invariance for the covariance kernel of X or the reference measure along which cos(βX) is integrated. To this purpose we establish by induction a general formula for the cumulants of a random variable defined on a filtered probability space expressed in terms of brackets of a family of martingales; to the best of our knowledge, the recursion formula is new and might have other applications. We apply this formula to study the cumulants of (approximations of) ∫ cos(βX). To control all terms produced by the induction proceedure, we prove a refinement of classical electrostatic inequalities, which allows to bound the energy of configurations in terms of the Wasserstein distance between + and − charges.
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