Research Interests: Stochastic Process, Physics, Quantum Mechanics, Statistical Physics, Medicine, and 15 moreMathematical Sciences, Delay Differential Equation, Physical sciences, Time Delay, Oscillations, Physical, CHEMICAL SCIENCES, Nonlinear system, Markov Process, Differential equation, Control of Chaos, Correlation Dimension, Parametric analysis, Chaotic, and attractor
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We revisit our description of randomness in quantum processes that began in collaboration of Jean Ginibre. The calculations were performed on a worked example: the fluorescence of a single two-level atom pumped by a resonant laser field.... more
We revisit our description of randomness in quantum processes that began in collaboration of Jean Ginibre. The calculations were performed on a worked example: the fluorescence of a single two-level atom pumped by a resonant laser field. This pump laser is described classically (by a function, not an operator). Our aim is first to built a Kolmogorov-type equation (K-equation) for the atomic state, so that the two parameters θ, φ that define this density matrix are random functions of time, therefore the atomic density matrix is a random density matrix. Such an approach, initiated for gas kinetics, was not yet applied to quantum phenomena, whereas it is especially tailored to very quick events well separated (in time) like the quantum jumps observed in spontaneous emission of photons by an atom. Here, we try to clarify the basis of our statistical approach leading to the K-equation below, and we present the main results deduced from it. We explain finally that our approach can be int...
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The chaotic solutions of an equation such as d x d t + X ( t ) = k f [ x ( t − τ R ) ] ,(1) where kf is the linear delayed feedback with delay τR and strength k, are studied with both random signal theory (statistics) and deterministic... more
The chaotic solutions of an equation such as d x d t + X ( t ) = k f [ x ( t − τ R ) ] ,(1) where kf is the linear delayed feedback with delay τR and strength k, are studied with both random signal theory (statistics) and deterministic chaos (entropy and Lyapunov dimension).
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Research Interests: Applied Mathematics, Physics, Optics, Medical Imaging, Fiber Optics, and 15 moreTelecommunications, Nonlinear Optics, Photonics, Society, Optical, Light, Ring, Diffraction, Optical physics, Non Linear Optics, Electromagnetic Wave, VAPOR, Electrical And Electronic Engineering, Continuous Wave, and Amplitude
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National audienc
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Analyse Les systèmes, optiquement bistables dans le régime stationnaire, peuvent présenter un régime chaotique caractérisé par une dimension de Lyapunov élevée. Cette dimension, calculée numériquement, est pratiquement égale au nombre de... more
Analyse Les systèmes, optiquement bistables dans le régime stationnaire, peuvent présenter un régime chaotique caractérisé par une dimension de Lyapunov élevée. Cette dimension, calculée numériquement, est pratiquement égale au nombre de fois que le temps d’auto-corrélation de la force de réaction est contenu dans le retard. Cette loi qui s’interprète à l’aide d’une image très simple de la dynamique, devrait être valable pour tout processus à réaction retardée oscillante ou de courte portée et permettrait aux expérimentateurs d’estimer facilement la dimension des attracteurs chaotiques qu’ils sont susceptibles d’observer.
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Spatial rings have been observed under a wide variety of conditions.1 We treat the propagation of a near-resonance cw laser beam through sodium vapor, which impresses phase and amplitude changes upon the beam’s transverse profile leading... more
Spatial rings have been observed under a wide variety of conditions.1 We treat the propagation of a near-resonance cw laser beam through sodium vapor, which impresses phase and amplitude changes upon the beam’s transverse profile leading to spatial rings in the far field.2–4
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Transverse effects on the profile of an intense off-resonant cw light beam, propagating through a gazeous cell of length ℓ, are numerically displayed in both cases of the very small absorption length (α-1 « ℓ ) and the intermediate case... more
Transverse effects on the profile of an intense off-resonant cw light beam, propagating through a gazeous cell of length ℓ, are numerically displayed in both cases of the very small absorption length (α-1 « ℓ ) and the intermediate case (α-1 ~ ℓ). As predicted by the theory, self-focusing and spatial ringings are obtained. Moreover for αℓ ~ 1, these distorsions generally appear as a recurrent process.
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... See fig. 7. Handling eqs. (24) with eqs. (41) allows us to write FULL LENGTH ARTICLE Volume 87, number 5,6 OPTICS COMMUNICATIONS 9,15111,15221 Ilk, max 0 l~,max -(3H - fiH 15 February 1992 Fig. ... B. Ségard and B. Macke, Phys. Rev.... more
... See fig. 7. Handling eqs. (24) with eqs. (41) allows us to write FULL LENGTH ARTICLE Volume 87, number 5,6 OPTICS COMMUNICATIONS 9,15111,15221 Ilk, max 0 l~,max -(3H - fiH 15 February 1992 Fig. ... B. Ségard and B. Macke, Phys. Rev. 60 (1988), p. 412. ...
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The kinetics of the domain walls that occur in the degenerate optical parametric oscillator are studied within the propagation model. The formation of large intensity peaks for null and positive signal mistuning is shown to be associated... more
The kinetics of the domain walls that occur in the degenerate optical parametric oscillator are studied within the propagation model. The formation of large intensity peaks for null and positive signal mistuning is shown to be associated with a dynamical scaling law ~t1/3. In the parameter range where the degenerate optical parametric operator reduces to potential systems, the growth law
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Among theories of the physical world, quantum mechanics remains a topic of lively discussions on its so-called interpretation. For some it remains an open question to understand how deterministic equations of this theory, as established... more
Among theories of the physical world, quantum mechanics remains a topic of lively discussions on its so-called interpretation. For some it remains an open question to understand how deterministic equations of this theory, as established long ago, may combine with a fundamental uncertainty. We consider the process of spontaneous emission by an atom interacting with infinite number of degrees of freedom of the electromagnetic field. There is uncertainty in the evolution of the photo-emission process which was characterized as Markovian by using the equations of quantum mechanics when the decay of the atom is due to the coupling with the vacuum field. The Markovian property leads us naturally to describe spontaneous emission by using the classical Kolmogorov equation for the probability evolution of a parameter defining the state of the atom. We explain that Everett’s many-worlds interpretation weld together our description, and appears therefore as a consequence of the equations of qu...
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The randomness of some irreversible quantum phenomena is a central question because irreversible phenomena break quantum coherence and thus yield an irreversible loss of information. The case of quantum jumps observed in the fluorescence... more
The randomness of some irreversible quantum phenomena is a central question because irreversible phenomena break quantum coherence and thus yield an irreversible loss of information. The case of quantum jumps observed in the fluorescence of a single two-level atom illuminated by a quasi-resonant laser beam is a worked example where statistical interpretations of quantum mechanics still meet some difficulties because the basic equations are fully deterministic and unitary. In such a problem with two different time scales, the atom makes coherent optical Rabi oscillations between the two states, interrupted by random emissions (quasi-instantaneous) of photons where coherence is lost. To describe this system, we already proposed a novel approach, which is completed here. It amounts to putting a probability on the density matrix of the atom and deducing a general “kinetic Kolmogorov-like” equation for the evolution of the probability. In the simple case considered here, the probability ...
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A major question in our understanding of the fabric of the world is where the randomness of some quantum phenomena comes from and how to represent it in a rational theory. The statistical interpretation of quantum mechanics made its way... more
A major question in our understanding of the fabric of the world is where the randomness of some quantum phenomena comes from and how to represent it in a rational theory. The statistical interpretation of quantum mechanics made its way progressively since the early days of the theory. We summarize the main historical steps and then we outline how the randomness gains to be depicted by using tools adapted to Markov processes. We consider a model system corresponding to experimental situations, namely a single two-level atom submitted to a monochromatic light triggering transitions from the ground to the excited state. After a short summary of present quantum approaches, we explain how a general "kinetic-like" Kolmogorov equation yields the statistical properties of the fluorescent light radiated by the atom which makes at once Rabi oscillations between the two states, and random quantum jumps with photo-emission. As an exemple we give the probability distribution of the ti...
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In a recent paper we presented evidence for the occurence of Leray-like singularities with positive Sedov-Taylor exponent $\alpha$ in turbulent flows recorded in Modane's wind tunnel, by looking at simultaneous acceleration and... more
In a recent paper we presented evidence for the occurence of Leray-like singularities with positive Sedov-Taylor exponent $\alpha$ in turbulent flows recorded in Modane's wind tunnel, by looking at simultaneous acceleration and velocity records. Here we use another tool which allows to get other informations on the dynamics of turbulent bursts. We compare the structure functions for velocity and acceleration in the same turbulent flows. This shows the possible contribution of other types of self-similar solutions because this new study shows that statistics is seemingly dominated by singularities with small positive or even negative values of the exponent $\alpha$, that corresponds to "weakly singular" solutions with singular acceleration, and regular velocity. We present several reasons explaining that the exponent $\alpha$ derived from the structure functions curves, may look to be negative.
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A 1934 paper by Leray posed the question of the regularity of solutions of the dynamical equations for incompressible inviscid fluids with smooth initial data. Since there has been many attempts to answer this question. Leray examined the... more
A 1934 paper by Leray posed the question of the regularity of solutions of the dynamical equations for incompressible inviscid fluids with smooth initial data. Since there has been many attempts to answer this question. Leray examined the possibility of self-similar solutions becoming singular in finite time at a definite space-time location. We reexamine this question in the light of a thorough analysis of the equations for the self-similar solution in axisymmetric geometries with a dependence on a logarithm of time besides the one due to the transformation to self-similar variables.
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It has long been suspected that flows of incompressible fluids at very large or infinite Reynolds may present finite time singularities. We review briefly the theoretical situation on this point. Then we show that single point records of... more
It has long been suspected that flows of incompressible fluids at very large or infinite Reynolds may present finite time singularities. We review briefly the theoretical situation on this point. Then we show that single point records of velocity fluctuations in the Modane wind tunnel show correlations between large velocities and large accelerations that are in agreement with the scaling laws for such singularities as derived by Leray in 1934. Conversely the experimental correlations between velocity and acceleration are not explainable by Kolmogorov scalings. This implies in particular that the singularities cannot be seen as the end of a cascade in the sense of Kolmogorov, but are best described as singular events in the sense of Leray.
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ABSTRACT
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A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is... more
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is generically preceded by a precursor phase which is less rapid, that we characterize. In this model, if an external source of noise exist, the correlation length of the fluctuations increases before the transition, and its spectrum tends to drift towards lower frequencies. This change in the fluctuations could be a way of detecting catastrophic events before they happen.