Analytical Results for Multifractal Properties of Spectra of Quasiperiodic Hamiltonians near the Periodic Chain

The multifractal properties of the electronic spectrum of a general quasiperiodic chain are studied in first order in the quasiperiodic potential strength. Analytical expressions for the generalized dimensions are found and are in good agreement with numerical simulations. These first order results do not depend on the irrational incommensurability.Comment: 10 Pages in RevTeX, 2 Postscript figure

COLLAPSE AND EVAPORATION OF A CANONICAL SELF-GRAVITATING GAS

International audienceWe review the out-of-equilibrium properties of a self-gravitating gas of particles in the presence of a strong friction and a random force (canonical gas). We assume a bare diffusion coefficient of the form D(ρ) = T ρ 1/n , where ρ is the local particle density, so that the equation of state is P (ρ) = D(ρ)ρ. Depending on the spatial dimension d, the index n, the temperature T , and whether the system is confined to a finite box or not, the system can reach an equilibrium state, collapse or evaporate. This article focuses on the latter cases, presenting a complete dynamical phase diagram of the system

Fractional Poincaré inequalities for general measures

18 pages. Version 2 includes corrections of 2 misprints and an additionnal reference [BBCG08] providing a weaker condition (1.2) (none of these corrections modifies the main result nor its proof). Thanks to Arnaud Guillin for pointing out these corrections.International audienceWe prove a fractional version of Poincaré inequalities in the context of $\R^n$ endowed with a fairly general measure. Namely we prove a control of an $L^2$ norm by a non local quantity, which plays the role of the gradient in the standard Poincaré inequality. The assumption on the measure is the fact that it satisfies the classical Poincaré inequality, so that our result is an improvement of the latter inequality. Moreover we also quantify the tightness at infinity provided by the control on the fractional derivative in terms of a weight growing at infinity. The proof goes through the introduction of the generator of the Ornstein-Uhlenbeck semigroup and some careful estimates of its powers. To our knowledge this is the first proof of fractional Poincaré inequality for measures more general than Lévy measures

Exact solution of a model of time-dependent evolutionary dynamics in a rugged fitness landscape

A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The statistics of the number of changes of the dominant genotype from a finite set of genotypes are exactly obtained confirming existing conjectures based on numerics.Comment: 5 pages RevTex 2 figures .ep

Geometric study of a 2D tiling related to the octagonal quasiperiodic tiling

International audienceA quasicrystal built with three types of tiles is related to the well-known octagonal tiling. The relationships between both tilings are investigated. More precisely, we show that the coordinates of the vertices can be obtained in two different but equivalent ways. The structure factor is calculated exactly. We emphasize the difficulty one can have to define the order of the symmetry of a quasicrystal, from a practical point of view, exhibiting a quasiperiodic tiling whose spectrum has a « quasi » eight-fold symmetry. Finally, we show how to recover easily a class of octagonal-like quasicrystals.Au moyen de trois tuiles, nous construisons un pavage quasipériodique du plan, que nous relions au quasicristal octogonal. Ainsi, nous montrons que les coordonnées des nœuds peuvent être obtenues de deux manières différentes. Le facteur de structure est calculé exactement. Ce pavage qui possède « presque » une symétrie d'ordre huit, soulève la difficulté de la détermination pratique de la symétrie d'un quasicristal. Finalement, nous montrons comment construire une large classe de pavage du type de l'octogonal, à partir de ce nouveau pavage

Quantum Critical Scaling of Fidelity Susceptibility

The behavior of the ground-state fidelity susceptibility in the vicinity of a quantum critical point is investigated. We derive scaling relations describing its singular behavior in the quantum critical regime. Unlike it has been found in previous studies, these relations are solely expressed in terms of conventional critical exponents. We also describe in detail a quantum Monte Carlo scheme that allows for the evaluation of the fidelity susceptibility for a large class of many-body systems and apply it in the study of the quantum phase transition for the transverse-field Ising model on the square lattice. Finite size analysis applied to the so obtained numerical results confirm the validity of our scaling relations. Furthermore, we analyze the properties of a closely related quantity, the ground-state energy's second derivative, that can be numerically evaluated in a particularly efficient way. The usefulness of both quantities as alternative indicators of quantum criticality is examined.Comment: 13 pages, 7 figures. Published versio

Quantifying the biomimicry gap in biohybrid systems

Biohybrid systems in which robotic lures interact with animals have become compelling tools for probing and identifying the mechanisms underlying collective animal behavior. One key challenge lies in the transfer of social interaction models from simulations to reality, using robotics to validate the modeling hypotheses. This challenge arises in bridging what we term the "biomimicry gap", which is caused by imperfect robotic replicas, communication cues and physics constrains not incorporated in the simulations that may elicit unrealistic behavioral responses in animals. In this work, we used a biomimetic lure of a rummy-nose tetra fish (Hemigrammus rhodostomus) and a neural network (NN) model for generating biomimetic social interactions. Through experiments with a biohybrid pair comprising a fish and the robotic lure, a pair of real fish, and simulations of pairs of fish, we demonstrate that our biohybrid system generates high-fidelity social interactions mirroring those of genuine fish pairs. Our analyses highlight that: 1) the lure and NN maintain minimal deviation in real-world interactions compared to simulations and fish-only experiments, 2) our NN controls the robot efficiently in real-time, and 3) a comprehensive validation is crucial to bridge the biomimicry gap, ensuring realistic biohybrid systems