Search results for "chaos"
showing 10 items of 106 documents
The Emergence of Chaos in Quantum Mechanics
2020
Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schrö
Le Chaosmos oulipien
2009
Le chaosmos, néologisme jamesien soulignant la prolifération des interprétations possibles d’un texte, semble devoir s’incarner de manière originale dans la production oulipienne: au désordre créatif l’écriture oulipienne impose la contrainte qui mène l’œuvre à l’ordre, c’est-à-dire à sa correcte appréciation. C’est le choix stylistique qui consent aux oulipiens de renouveler la création par l’intervention d’une écriture énigmatique parfois compliqué d’une énigme fictionnelle. C’est dans les policiers oulipiens que l’acte même d’écrire devient procédé chaosmotique. The cahosmos, James’s neologism used to point out the proliferations of all the possible interpretations and adaptations of a t…
Bill2d - a software package for classical two-dimensional Hamiltonian systems
2015
Abstract We present Bill2d , a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. Bill2d can be used for various billiard and diffusion problems with one or more charged particles with interactions, different external potentials, an external magnetic field, periodic and open boundaries, etc. The software package can also calculate many key quantities in complex systems such as Poincare sections, survival probabilities, and diffusion coefficients. While aiming at a large class of applicable systems, the code also strives for ease-of-use, efficiency, and modularity for the implementation of additional features. The package comes along with a use…
$L_2$-variation of L\'{e}vy driven BSDEs with non-smooth terminal conditions
2016
We consider the $L_2$-regularity of solutions to backward stochastic differential equations (BSDEs) with Lipschitz generators driven by a Brownian motion and a Poisson random measure associated with a L\'{e}vy process $(X_t)_{t\in[0,T]}$. The terminal condition may be a Borel function of finitely many increments of the L\'{e}vy process which is not necessarily Lipschitz but only satisfies a fractional smoothness condition. The results are obtained by investigating how the special structure appearing in the chaos expansion of the terminal condition is inherited by the solution to the BSDE.
Erratum to “Simulation of BSDEs with jumps by Wiener Chaos expansion” [Stochastic Process. Appl. 126 (2016) 2123–2162]
2017
Abstract We correct Proposition 2.9 from “Simulation of BSDEs with jumps by Wiener Chaos expansion” published in Stochastic Processes and their Applications, 126 (2016) 2123–2162. The proposition which provides an expression for the expectation of products of multiple integrals (w.r.t. Brownian motion and compensated Poisson process) requires a stronger integrability assumption on the kernels than previously stated. This does not affect the remaining results of the article.
Simulation of BSDEs with jumps by Wiener Chaos Expansion
2016
International audience; We present an algorithm to solve BSDEs with jumps based on Wiener Chaos Expansion and Picard's iterations. This paper extends the results given in Briand-Labart (2014) to the case of BSDEs with jumps. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. Concerning the error, we derive explicit bounds with respect to the number of chaos, the discretization time step and the number of Monte Carlo simulations. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.
Deformation Quantization by Moyal Star-Product and Stratonovich Chaos
2012
We make a deformation quantization by Moyal star-product on a space of functions endowed with the normalized Wick product and where Stratonovich chaos are well defined.
Thermalization and condensation in an incoherently pumped passive optical cavity
2011
International audience; We study theoretically and numerically the condensation and the thermalization of classical optical waves in an incoherently pumped passive Kerr cavity. We show that the dynamics of the cavity exhibits a turbulent behavior that can be described by the wave turbulence theory. A mean-field kinetic equation is derived, which reveals that, in its high finesse regime, the cavity behaves essentially as a conservative Hamiltonian system. In particular, the intracavity turbulent field is shown to relax adiabatically toward a thermodynamic equilibrium state of energy equipartition. As a consequence of this effect of wave thermalization, the incoherent optical field undergoes …
From equilibrium to chaos and back : methodological evaluation of research of the majority rule
2000
According to the canonical model situated at the heart of the " economic " - or, as the political scientists prefer to call it, rational-choice - theory of (democratic) politics, whenever the matter to be decided raises, or consists of, at least two distinct issues, it is generally impossible to reach a determinate decision by using the majority rule. This problem, referred to as that of disequilibrium, equilibrium instability, or even"chaos", was first underplayed and then deemed ominous to the point of seriously undermining the development prospects of the whole theory. However, more recently, the concern it was the source o f until the 1980s has given way to a state of renewed confidence…
Temporal incoherent solitons supported by a defocusing nonlinearity with anomalous dispersion
2012
http://pra.aps.org/; International audience; We study temporal incoherent solitons in noninstantaneous response nonlinear media. Contrarily to the usual temporal soliton, which is known to require a focusing nonlinearity with anomalous dispersion, we show that a highly noninstantaneous nonlinear response leads to incoherent soliton structures which require the inverted situation: In the focusing regime (and anomalous dispersion) the incoherent wave packet experiences an unlimited spreading, whereas in the defocusing regime (still with anomalous dispersion) the incoherent wave packet exhibits a self-trapping. These counterintuitive results are explained in detail by a long-range Vlasov formu…