Intensity statistics of branched flow

Branched flow is a universal phenomenon of particle and wave flows which are subjected to weak, correlated disorder. It has been observed on length scales ranging from a few micrometres, affecting the transport properties of semiconductor devices [1], up to several thousand kilometres, influencing sound propagation through the ocean [2]. It is also responsible for the appearance of large and hazardous freak waves and tsunamis [3]. While the statistics of the number of such branches has recently been calculated [4], the influence on the statistics of the intensity of the waves remains an open question [5]. Here, we show how the classical ray intensity impacts on the wave intensity statistics, and illuminate the role played by the decoherence of the wavefunction.\\ {[}1{]} Topinka et al., Nature 410, 183 (2001), Jura et al., Nat. Phys. 3, 841 (2007)\\ {[}2{]} Wolfson \& Tomsovich, J. Acous. Soc. Am. 109, 2693 (2001)\\ {[}3{]} Berry, Proc. R. Soc. A 463, 3055 (2007); Heller et al., J. Geophys. Res. 113, C09023 (2008)\\ {[}4{]} Metzger, Fleischmann and Geisel, Phys. Rev. Lett. 105, 020601 (2010)\\ {[}5{]} H\"ohmann et al., Phys. Rev. Lett. 104, 093901 (2010), Arecchi et al., Phys. Rev. Lett. 106, 153901 (2011), Ying et al., Nonlinearity 24, R67 (2011)