Laboratoire de Physique Théorique
Toulouse - UMR 5152

Rainbows, bright lines on the bottom of swimming pools, rogue waves at sea, gravitational lensing : these are all examples of natural focusing. In optics they are known as caustics and are the places where geometric ray theory predicts infinite intensity forcing us to use wave theory get sensible answers. Since the 1970s it has been realized that there is an underlying order to these structures given by catastrophe theory [R. Thom (1975), V.I. Arnol’d (1975)]. There are only seven distinct catastrophes that can occur in 3+1 dimensions. They are generic (need no special symmetry) and they are insensitive to perturbations ("structurally stable") which makes them universal. In this talk I will argue that catastrophe theory should be extended to include quantum catastrophes, i.e. places where wave theory fails and we are forced to second-quantize to remove a singularity (in the case of optics this forces us to introduce the photon). I will give examples from atom optics and the dynamics of Bose-Einstein condensates in lattices following a quench to illustrate the basic idea.