Propagation effects on the breakdown of a linear amplifier model

Complex-mass Sehrödinger equation driven by the square of a Gaussian field

Philippe Mounaix, Pierre Collet, Joel Lebowitz

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Solutions to the equation ∂tε(x, t) - i/2mΔε(x, t) = λ|S(x, t)|2 ε(x, t) are investigated, where S(x, t) is a complex Gaussian field with zero mean and specified covariance, and m ≠ 0 is a complex mass with Im(m) > 0. For real m this equation describes the backscattering of a smoothed laser beam by an optically active medium. Assuming that S(x, t) is the sum of a finite number of independent complex Gaussian random variables, we obtain an expression for the value of at which the qth moment of |ε(x, t)| w.r.t. the Gaussian field S diverges. This value is found to be less or equal for all m ≠ 0, Im(m) ≥ 0 and |m| < + ∞ than for |m| = +∞, i.e. when the Δε term is absent. Our solution is based on a distributional formulation of the Feynman path-integral and the Paley-Wiener theorem.

Original languageEnglish (US)
Pages (from-to)741-758
Number of pages18
JournalCommunications In Mathematical Physics
Volume264
Issue number3
DOIs
StatePublished - Jun 1 2006

Fingerprint

Gaussian Fields
Breakdown
Propagation
Paley-Wiener Theorem
Feynman Path Integral
Backscattering
Diverge
Laser Beam
Random variable
Model
Moment
Formulation
Zero
Term

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Propagation effects on the breakdown of a linear amplifier model : Complex-mass Sehrödinger equation driven by the square of a Gaussian field. / Mounaix, Philippe; Collet, Pierre; Lebowitz, Joel.

In: Communications In Mathematical Physics, Vol. 264, No. 3, 01.06.2006, p. 741-758.

Research output: Contribution to journalArticle

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