Note on a diffraction-amplification problem
Mathematical Physics
2009-11-10 v1 math.MP
Abstract
We investigate the solution of the equation \partial_t E(x,t)-iD\partial_x^2 E(x,t)= \lambda |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 \lambda_c at which <|E|> diverges for t>=1 (in suitable units), is always less or equal for D>0 than D=0.
Cite
@article{arxiv.math-ph/0403018,
title = {Note on a diffraction-amplification problem},
author = {Philippe Mounaix and Joel L. Lebowitz},
journal= {arXiv preprint arXiv:math-ph/0403018},
year = {2009}
}
Comments
REVTeX file, 8 pages, submitted to Journal of Physics A