Universal statistics of branched flows.
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.
Metzger
Jakob J
JJ
Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstraße 10, 37073 Göttingen, Germany.
Fleischmann
Ragnar
R
Geisel
Theo
T