Elementary branching: waves, rays, decoherence

Abstract

The ‘elementary particle’ of branched flow is the splitting of waves and rays into localised branches at an individual cusped caustic. Localisation is the result of noise in the incident beam: decoherence for waves, here modelled analytically by random phases, or irregularity in the rays, here modelled by transverse smoothing. The two models coincide as the localisation emerges with increasing noise.

Acoustic as an Abelian U(1) local gauge theory

“…The smooth single-valued function of the complex scalar field will give rise to the existence of the singularities of the phase 4-8 . This phase singularity 5 where the phase is undefined 5 or indeterminate 6,9 have been shown to have a well-defined mathematical structure 9 .…”

“…As the Maxwell's linear theory 12 , the Maxwell-like theory of acoustic could have the knot. In fact, an ultrasonic pulse, containing, say, ten quasi-sinusoidal oscillations, is reflected in air from a rough surface, it is observed experimentally that the scattered wave train contains dislocations 6 . We have a plan to write this topics in a separated article.…”