Note on a diffraction-amplification problem
Philippe Mounaix, Joel L. Lebowitz
Abstract
We investigate the solution of the equation ∂t E(x,t)-iD∂x2 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 λc 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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