Branched Flow

From Branched Flow to Superwires in Periodic Potentials

“…[23] and below) with an amplitude that corresponds to half of the energy of the wave packet. The characteristics of the branching produced by this random potential are similar to the previous findings [1].…”

“…To analyze the branched flow in a periodic system further, let us consider the classical kick and drift map [1]. It is an area preserving time-discrete map based on Hamilton's equation of motion defined by where x and p correspond to the trajectory's position and momentum, n is a natural number playing the role of discrete time, and V is a potential depending on the position.…”

“…Previously, [1], the "kick" used randomly chosen parameters, but here we repeatedly use the same spatially periodic potential, writing…”

“…Branched flow is a common phenomenon of wave dynamics: when a wave impinges a weakly refractive medium, it can create an intensity pattern akin to the shadow of a tree [1].…”

Elementary branching: waves, rays, decoherence

“…The remarkable phenomenon of branched flow, in which waves split repeatedly while travelling through a smoothly and gently disordered refracting medium, has been studied in different contexts and from different perspectives. Examples where branching occurs (mostly two-dimensonal) are: electrons issuing from a quantum point contact [1][2][3], tsunamis passing over an ocean whose depth varies [4], rogue waves [5], microwaves [6], and recently light, in beautiful experiments and simulations [7] with incident beams and plane waves confined within soap films whose thickness varies. Investigations have centred on several aspects, including: statistics [8][9][10][11][12], ray and wave descriptions [10], controlling flow along the branches [13], and persisting localisation of the branches [7].…”