Uniformity transition for ray intensities in random media

作者：Pradas Marc^*; Pumir Alain; Wilkinson Michael

来源：Journal of Physics A-Mathematical and Theoretical, 2018, 51(15): 155002.

DOI：10.1088/1751-8121/aab161

• random media
• intensity fluctuautions
• phase transition
• large deviations

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 = Lambda(N), for some Lambda > 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 -> infinity, and a phase where the S has large fluctuations, for which we provide a large deviation analysis.

• 出版日期2018-4-13