Search results for "Mathematical physics"
showing 10 items of 2687 documents
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…
Spatiotemporal optical solitons in nonlinear dissipative media: From stationary light bullets to pulsating complexes
2007
Nonlinear dissipative systems display the full (3+1) D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1) D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation. © 2007 American Institute of Physics.
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.
18 parameter deformations of the Peregrine breather of order 10 solutions of the NLS equation
2015
We present here new solutions of the focusing one-dimensional nonlinear Schrödinger (NLS) equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric rings as found for the lower-orders.
Isotope removal experiment in JET-ILW in view of T-removal after the 2nd DT campaign at JET
2022
Abstract A sequence of fuel recovery methods was tested in JET, equipped with the ITER-like beryllium main chamber wall and tungsten divertor, to reduce the plasma deuterium concentration to less than 1% in preparation for operation with tritium. This was also a key activity with regard to refining the clean-up strategy to be implemented at the end of the 2nd DT campaign in JET (DTE2) and to assess the tools that are envisaged to mitigate the tritium inventory build-up in ITER. The sequence began with 4 days of main chamber baking at 320 °C, followed by a further 4 days in which Ion Cyclotron Wall Conditioning (ICWC) and Glow Discharge Conditioning (GDC) were applied with hydrogen fuelling,…
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…
Parabolic equations with nonlinear singularities
2011
Abstract We show the existence of positive solutions u ∈ L 2 ( 0 , T ; H 0 1 ( Ω ) ) for nonlinear parabolic problems with singular lower order terms of the asymptote-type. More precisely, we shall consider both semilinear problems whose model is { u t − Δ u + u 1 − u = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , and quasilinear problems having natural growth with respect to the gradient, whose model is { u t − Δ u + ∣ ∇ u ∣ 2 u γ = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , with γ > 0 . Moreover, we prove a comparison principle and, as an application, we study the asymptotic behav…
Conceptual design and simulation of a water Cherenkov muon veto for the XENON1T experiment
2014
XENON is a direct detection dark matter project, consisting of a time projection chamber (TPC) that uses xenon in double phase as a sensitive detection medium. XENON100, located at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy, is one of the most sensitive experiments of its field. During the operation of XENON100, the design and construction of the next generation detector (of ton-scale mass) of the XENON project, XENON1T, is taking place. XENON1T is being installed at LNGS as well. It has the goal to reduce the background by two orders of magnitude compared to XENON100, aiming at a sensitivity of $2 \cdot 10^{-47} \mathrm{cm}^{\mathrm{2}}$ for a WIMP mass of 50 GeV/c$^{2}$. With…
Comparison between simulated and observed LHC beam backgrounds in the ATLAS experiment at E beam =4 TeV
2018
Results of dedicated Monte Carlo simulations of beam-induced background (BIB) in the ATLAS experiment at the Large Hadron Collider (LHC) are presented and compared with data recorded in 2012. During normal physics operation this background arises mainly from scattering of the 4 TeV protons on residual gas in the beam pipe. Methods of reconstructing the BIB signals in the ATLAS detector, developed and implemented in the simulation chain based on the FLUKA Monte Carlo simulation package, are described. The interaction rates are determined from the residual gas pressure distribution in the LHC ring in order to set an absolute scale on the predicted rates of BIB so that they can be compared qua…