arXiv subjects

Philippe Mounaix

Publications and source records attributed to Philippe Mounaix.

26 records · Page 2Linked to original sources

arXiv2010

Diffraction controlled backscattering threshold and application to Raman gap

The range of stimulated Raman scattering (SRS) frequencies covers a domain which at the low end abuts half the laser frequency, omega_0 / 2, according to the simplest SRS theories, corresponding to scatter from electron densities near 1/4 critical. Experiments, on the other hand, clearly point to a frequency gap: SRS is not observed at frequencies close to and above omega_0 / 2, indicating a drastic disruption of scatter from Langmuir waves as electron densities approaches 1/4 critical from below. Several one-dimensional mechanisms, linear and nonlinear, have been proposed to explain this "Raman gap". In this paper we release the one-dimensional constraint by allowing diffraction of the scattered light. In the linear convective regime we find that diffractive effects on SRS from a wide speckled laser beam tend to increase the SRS threshold with increase of density, so long as the interaction length is comparable to or larger than a speckle length. This may lead to a new, diffraction controlled, contribution to the Raman gap.

physics.plasm-ph↗

arXiv2010

Wave localization does not affect the breakdown of a Schrödinger-type amplifier driven by the square of a Gaussian field

We study the divergence of the solution to a Schrödinger-type amplifier driven by the square of a Gaussian noise in presence of a random potential. We follow the same approach as Mounaix, Collet, and Lebowitz (MCL) in terms of a distributional formulation of the amplified field and the use of the Paley-Wiener theorem [Commun. Math. Phys. {\bf 264}, 741-758 (2006) and {\bf 280}, 281-283 (2008)]. Our results show that the divergence is not affected by the random potential, in the sense that it occurs at exactly the same coupling constant as what was found by MCL without a potential. It follows {\it a fortiori} that the breakdown of the amplifier is not affected by the possible existence of a localized regime in the amplification free limit.

math-ph↗

arXiv2010

Nonequilibrium stationary state of a truncated stochastic NLSE: I. Formulation and mean field approximation

We investigate the stationary state of a model system evolving according to a modified focusing truncated nonlinear Schrödinger equation (NLSE) used to describe the envelope of Langmuir waves in a plasma. We restrict the system to have a finite number of normal modes each of which is in contact with a Langevin heat bath at temperature $T$. Arbitrarily large realizations of the field are prevented by restricting each mode to a maximum amplitude. We consider a simple modeling of wave-breaking in which each mode is set equal to zero when it reaches its maximum amplitude. Without wave-breaking the stationary state is given by a Gibbs measure. With wave-breaking the system attains a nonequilibrium stationary state which is the unique invariant measure of the time evolution. A mean field analysis shows that the system exhibits a transition from a regime of low field values at small $|λ|$, to a regime of higher field values at large $|λ|$, where $λ<0$ specifies the strength of the nonlinearity in the focusing case. Field values at large $|λ|$ are significantly smaller with wave-breaking than without wave-breaking.

math-ph↗

arXiv2009

Note on the Transition to Intermittency for the exponential of the Square of a Steinhaus Series

Intermittency of $\mathcal{E}_N(x,g)=\exp\lbrack g| S_N(x)|^2\rbrack$ as $N\to +\infty$ is investigated on a $d$-dimensional torus $Λ$, when $S_N(x)$ is a finite Steinhaus series of $(2N+1)^d$ terms normalized to $<| S_N(x)|^2> =1$. Assuming ergodicity of $\mathcal{E}_N(x,g)$ as $N\to +\infty$ in the domain $g<1$, where $\lim_{N\to +\infty}<\mathcal{E}_N(g)>$ exists, transition to intermittency is proved as $g$ increases past the threshold $g_{th}=1$. This transition goes together with a transition from (assumed) ergodicity at $g \rbrack^{-1}\int_Λ\mathcal{E}_N(x,g) d^dx=0$ at $g>g_{th}$. In this asymptotic sense one can say that ergodicity is lost as $g$ increases past the value $g=1$.

math-ph↗

arXiv2007

Erratum: Propagation Effects on the Breakdown of a Linear Amplifier Model: Complex-Mass Schrodinger Equation Driven by the Square of a Gaussian Field

The proof of the inequality $λ_{q}(x,t)\le (qμ_{x,t} -0^+)^{-1}$ [p 750, below Eq. (29)] is based on the statement that ${\cal E}(x,t;s)$ is an entire function of $s\in {\mathbb C}^M$ [see below Eq. (30)]. But according to Equation (9) and Lemma 1, all we know is that ${\cal E}(x,t;s)$ is an entire function of $k(s)\in {\mathbb R}^N$. Nevertheless, the above inequality holds, hence the proposition 1.

math-ph↗

arXiv2006

Propagation Effects on the Breakdown of a Linear Amplifier Model: Complex-Mass Schrodinger Equation Driven by the Square of a Gaussian Field

Solutions to the equation $\partial_t{\cal E}(x,t)-\frac{i}{2m}Δ{\cal E}(x,t)=λ| S(x,t)|^2{\cal E}(x,t)$ are investigated, where $S(x,t)$ is a complex Gaussian field with zero mean and specified covariance, and $m\ne 0$ is a complex mass with ${\rm Im}(m)\ge 0$. For real $m$ this equation describes the backscattering of a smoothed laser beam by an optically active medium. Assuming that $S(x,t)$ is the sum of a finite number of independent complex Gaussian random variables, we obtain an expression for the value of $λ$ at which the $q$-th moment of $| {\cal E}(x,t)|$ w.r.t. the Gaussian field $S$ diverges. This value is found to be less or equal for all $m\ne 0$, ${\rm Im}(m)\ge 0$ and $| m| <+\infty$ than for $| m| =+\infty$, i.e. when the $Δ{\cal E}$ term is absent. Our solution is based on a distributional formulation of the Feynman path-integral and the Paley-Wiener theorem.

math-ph↗

arXiv2004

Note on a diffraction-amplification problem

We investigate the solution of the equation \partial_t E(x,t)-iD\partial_x^2 E(x,t)= λ|S(x,t)|^2 E(x,t)$, for x in a circle and S(x,t) a Gaussian stochastic field with a covariance of a particular form. It is shown that the coupling λ_c at which <|E|> diverges for t>=1 (in suitable units), is always less or equal for D>0 than D=0.

math-ph↗

arXiv2002

Cosmological Equations for a Thick Brane

Generalized Friedmann equations governing the cosmological evolution inside a thick brane embedded in a five-dimensional Anti-de Sitter spacetime are derived. These equations are written in terms of four-dimensional effective brane quantities obtained by integrating, along the fifth dimension, over the brane thickness. In the case of a Randall-Sundrum type cosmology, different limits of these effective quantities are considered yielding cosmological equations which interpolate between the thin brane limit (governed by unconventional brane cosmology), and the opposite limit of an ``infinite'' brane thickness corresponding to the familiar Kaluza-Klein approach. In the more restrictive case of a Minkowski bulk, it is shown that no effective four-dimensional reduction is possible in the regimes where the brane thickness is not small enough.

gr-qc↗