title: Universal statistics of branched flows.
abstract: Even very weak correlated disorder potentials can cause extreme fluctuations in Hamiltonian flows. In two dimensions this leads to a pronounced branching of the flow. Although present in a great variety of physical systems, a quantitative theory of the branching statistics is lacking. Here, we derive an analytical expression for the number of branches valid for all distances from a source. We also derive the scaling relations that make this expression universal for a wide range of random potentials. Our theory has possible applications in many fields ranging from semiconductor to geophysics.
authors.affiliation: Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstraße 10, 37073 Göttingen, Germany.
authors.forename: Jakob J
authors.initials: JJ
authors.lastname: Metzger
authors.forename: Ragnar
authors.initials: R
authors.lastname: Fleischmann
authors.forename: Theo
authors.initials: T
authors.lastname: Geisel