English

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