Note on a diffraction-amplification problem

Details Note on a diffraction-amplification problem Note on a diffraction-amplification problem

2004-03-12

arxiv.org/abs/math-ph/0403018v1

Journal of Physics A: Mathematical and General, volume 37, issue 20, pp. 5289-5294 (2004)

Physics

Mathematical Physics

REVTeX file, 8 pages, submitted to Journal of Physics A

Scientific paper

10.1088/0305-4470/37/20/002

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.

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