Morphology of a quantum catastrophe

Thom's seven elementary catastrophes are the only structurally stable singularities in up to four dimensions \cite{thom75}. Their stability against perturbations removes any symmetry requirement which accounts for their ubiquity in nature, e.g.\ as caustics. Examples include rainbows \cite{nye99}, the twinkling of starlight \cite{berry77}, rogue waves at sea \cite{hohmann10} and structure formation in the universe \cite{Zeldovich82}. At large scales the intensity appears to diverge on a caustic, but at the scale of a wavelength interference smooths the singularity and produces characteristic diffraction patterns \cite{arnold75,berry76,trinkhaus77,handbook}. At subwavelength scales wave catastrophes are organized by an underlying lattice of dislocations (nodes) around each of which the wave function circulates as a vortex \cite{pearcey46,Nye74}. Here we study the morphology of a third generation beyond geometric and wave catastrophes, called quantum catastrophes, which are singularities of classical fields. They are regulated by quantizing the excitations, i.e.\ second quantization \cite{leonhardt02,berry04,berry08,odell12}, and live in Fock space which, being fundamentally discrete, leads to core-less discretized vortices. These are created or annihilated in pairs as the number of quanta is varied.