Uniformity transition for ray intensities in random media. (15th March 2018)

• Record Type: Journal Article
• Authors: Pradas, Marc; Pumir, Alain; Wilkinson, Michael
• Is Part Of: Journal of physics. Volume 51:Number 15(2018)
• Publication Date: 2018-03-15
• Subjects: random media -- intensity fluctuautions -- phase transition -- large deviations; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aab161
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: This paper analyses a model for the intensity of distribution for rays propagating without absorption in a random medium. The random medium is modelled as a dynamical map. After N iterations, the intensity is modelled as a sum S of N contributions from different trajectories, each of which is a product of N independent identically distributed random variables x k, representing successive focussing or de-focussing events. The number of ray trajectories reaching a given point is assumed to proliferate exponentially: N = Λ N, for some Λ > 1 . We investigate the probability distribution of S . We find a phase transition as parameters of the model are varied. There is a phase where the fluctuations of S are suppressed as N → ∞, and a phase where the S has large fluctuations, for which we provide a large deviation analysis.