%0 Book Section %1 statphys23_0373 %A Elskens, Y. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K box chaos interaction plasma propagation quasilinear resonance statphys23 theory topic-3 turbulence wave-particle weak %T Loss of correlations between N particles in a single chaotic forcefield %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=373 %X The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited with nonperturbative techniques of stochastic differential equations. When the wavefield has a single wavenumber $\kappa$ and white noise time dependence, it is represented as $(q/m) d E (\xi,t) = (\xi) \, d W'_t + (\xi) \, d W''_t$. For each particle the velocity is shown to be a Wiener process with the quasilinear diffusion coefficient $\alpha^2$. The joint $N$ velocity processes define a martingale, the components of which become independent in the strong noise limit $ınfty$, ensuring propagation of chaos in this system. The connection with the concept of resonance box is discussed. Full nonlinear dynamics results are compared with the linearization around particle ballistic motions. The key quantity in the analysis is the relative velocity between two particles.

@incollection{statphys23_0373, abstract = {The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited with nonperturbative techniques of stochastic differential equations. When the wavefield has a single wavenumber $\kappa$ and white noise time dependence, it is represented as $(q/m) {\mathrm d} E (\xi,t) = \alpha [\cos (\kappa \xi) \, {\mathrm d} W'_t + \sin (\kappa \xi) \, {\mathrm d} W''_t]$. For each particle the velocity is shown to be a Wiener process with the quasilinear diffusion coefficient $\sim \alpha^2$. The joint $N$ velocity processes define a martingale, the components of which become independent in the strong noise limit $\alpha \to \infty$, ensuring propagation of chaos in this system. The connection with the concept of resonance box is discussed. Full nonlinear dynamics results are compared with the linearization around particle ballistic motions. The key quantity in the analysis is the relative velocity between two particles.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Elskens, Y.}, biburl = {https://www.bibsonomy.org/bibtex/2f7ad511fc90c585faa45e7d80c5e4825/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {e93963b19a44619c8b6ccb689051bbf3}, intrahash = {f7ad511fc90c585faa45e7d80c5e4825}, keywords = {box chaos interaction plasma propagation quasilinear resonance statphys23 theory topic-3 turbulence wave-particle weak}, month = {9-13 July}, timestamp = {2007-06-20T10:16:18.000+0200}, title = {Loss of correlations between N particles in a single chaotic forcefield}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=373}, year = 2007 }