Search results for "math-ph"
showing 10 items of 525 documents
Kontsevich and Takhtajan construction of star product on the Poisson Lie group GL(2)
2001
Comparing the star product defined by Takhtajan on the Poisson-Lie group GL(2) and any star product calculated from the Kontsevich's graphs (any ''K-star product'') on the same group, we show, by direct computation, that the Takhtajan star product on GL(2) can't be written as a K-star product.
Painlevé-II approach to binary black hole merger dynamics: universality from integrability
2022
The binary black hole merger waveform is both simple and universal. Adopting an effective asymptotic description of the dynamics, we aim at accounting for such universality in terms of underlying (effective) integrable structures. More specifically, under a ``wave-mean flow'' perspective, we propose that fast degrees of freedom corresponding to the observed waveform would be subject to effective linear dynamics, propagating on a slowly evolving background subject to (effective) non-linear integrable dynamics. The Painlevé property of the latter would be implemented in terms of the so-called Painlevé-II transcendent, providing a structural link between i) orbital (in particular, EMRI) dynami…
On Einstein bilinear form
2012
From physical motivations and from geometrical interpretations of the Einstein equations, we give a justi cation of the non-triviality and non-degeneracy of Einstein bilinear form introduced in [1].
Modélisation auto cohérente du comportement viscoplastique en grandes déformations et à grandes vitesses d'un métal cubique centré préalablement choq…
2005
International audience
From finite-gap solutions of KdV in terms of theta functions to solitons and positons
2010
We degenerate the finite gap solutions of the KdV equation from the general formulation in terms of abelian functions when the gaps tends to points, to recover solutions of KdV equations in terms of wronskians called solitons or positons. For this we establish a link between Fredholm determinants and Wronskians.
On the analytical expression of the multicompacton and some exact compact solutions of a nonlinear diffusive Burgers’type equation
2018
International audience; We consider the nonlinear diffusive Burgers' equation as a model equation for signals propagation on the nonlinear electrical transmission line with intersite nonlinearities. By applying the extend sine-cosine method and using an appropriate modification of the Double-Exp function method, we successfully derived on one hand the exact analytical solutions of two types of solitary waves with strictly finite extension or compact support: kinks and pulses, and on the other hand the exact solution for two interacting pulse solitary waves with compact support. These analytical results indicate that the speed of the pulse compactons doesn't depends explicitly on the pulse a…
Nonlinear topological symmetry protection in a dissipative system
2023
We report an experimental and theoretical investigation of a system whose dynamics is dominated by an intricate interplay between three key concepts of modern physics: topology, nonlinearity, and spontaneous symmetry breaking. The experiment is based on a two-mode coherently-driven optical resonator in which photons interact through the Kerr nonlinearity. In presence of a phase defect between the modes, a nonlinear attractor develops, which confers a synthetic M\"obius topology to the modal structure of the system. That topology is associated with an inherently protected exchange symmetry between the modes, enabling the realization of spontaneous symmetry breaking in ideal, bias-free, condi…
Modèles quantiques à deux états avec croisements de niveaux décrits par les fonctions de Heun
2019
The thesis is devoted to the fundamental problem of excitation and manipulation of quantum systems, having discrete energy spectrum, via external laser fields. We examine the semiclassical time- dependent quantum two-state problem, when the external electromagnetic field is resonant or quasi-resonant for some two of many levels of the system. The focus of the thesis is on the analytic description of the non- adiabatic evolution of quantum systems subject to excitation by level-crossing field configurations. In the present thesis we classify the complete set of the semiclassical time-dependent quantum two-state models solvable in terms of the five function of the Heun class.Main results of t…
Quantizations from reproducing kernel spaces
2012
Abstract The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of L 2 ( C , d 2 z / π ) based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family depending on a nonnegative parameter s . We examine some interesting issues, mainly related to CS quantization, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules. The question of mathematical and physical equivalences between the s -dependent quantizations is also considered.
Acoustic Topological Circuitry in Square and Rectangular Phononic Crystals
2021
International audience; We systematically engineer a series of square and rectangular phononic crystals to create experimental realizations of complex topological phononic circuits. The exotic topological transport observed is wholly reliant upon the underlying structure which must belong to either a square or rectangular lattice system and not to any hexagonal-based structure. The phononic system chosen consists of a periodic array of square steel bars which partitions acoustic waves in water over a broadband range of frequencies (∼0.5MHz). An ultrasonic transducer launches an acoustic pulse which propagates along a domain wall, before encountering a nodal point, from which the acoustic si…