Note on a diffraction-amplification problem

Philippe Mounaix; Joel L. Lebowitz

doi:10.1088/0305-4470/37/20/002

Note on a diffraction-amplification problem

Philippe Mounaix
, Joel L. Lebowitz

Rutgers University–New Brunswick

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We investigate the solution of the equation ∂_tε(x, t) - iD∂_x²ε(x, t) = λ|S(x, t)| ²ε(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 〈|ε|〉 diverges for t ≥ 1 (in suitable units), is always less or equal for D > 0 than D = 0.

langue originale	Anglais
Pages (de - à)	5289-5294
Nombre de pages	6
journal	Journal of Physics A: Mathematical and General
Volume	37
Numéro de publication	20
Les DOIs	https://doi.org/10.1088/0305-4470/37/20/002
état	Publié - 21 mai 2004

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10.1088/0305-4470/37/20/002

Contient cette citation

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title = "Note on a diffraction-amplification problem",

abstract = "We investigate the solution of the equation ∂tε(x, t) - iD∂x2ε(x, t) = λ|S(x, t)| 2ε(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 〈|ε|〉 diverges for t ≥ 1 (in suitable units), is always less or equal for D > 0 than D = 0.",

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N2 - We investigate the solution of the equation ∂tε(x, t) - iD∂x2ε(x, t) = λ|S(x, t)| 2ε(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 〈|ε|〉 diverges for t ≥ 1 (in suitable units), is always less or equal for D > 0 than D = 0.

AB - We investigate the solution of the equation ∂tε(x, t) - iD∂x2ε(x, t) = λ|S(x, t)| 2ε(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 〈|ε|〉 diverges for t ≥ 1 (in suitable units), is always less or equal for D > 0 than D = 0.

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Note on a diffraction-amplification problem

Résumé

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