Elementary branching: waves, rays, decoherence

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. (paper)