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Note on a diffraction-amplification problem

Philippe Mounaix·Joel L. Lebowitz
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Abstract

We investigate the solution of the equation \partial_t E(x,t)-iD\partial_x^2 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 λ_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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Philippe Mounaix, Joel L. Lebowitz. 2004-03-12. Note on a diffraction-amplification problem. https://doi.org/10.1088/0305-4470%2F37%2F20%2F002

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