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

Research output: Contribution to journal › Article › peer-review

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 λ_c at which 〈|ε|〉 diverges for t ≥ 1 (in suitable units), is always less or equal for D > 0 than D = 0.

Original language	English
Pages (from-to)	5289-5294
Number of pages	6
Journal	Journal of Physics A: Mathematical and General
Volume	37
Issue number	20
DOIs	https://doi.org/10.1088/0305-4470/37/20/002
Publication status	Published - 21 May 2004

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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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AU - Lebowitz, Joel L.

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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.

U2 - 10.1088/0305-4470/37/20/002

DO - 10.1088/0305-4470/37/20/002

M3 - Article

AN - SCOPUS:2542621468

SN - 0305-4470

VL - 37

SP - 5289

EP - 5294

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 20

ER -

Note on a diffraction-amplification problem

Abstract

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