Caustics in quantum many-body dynamics

We describe a new class of nonequilibrium quantum many-body phenomena in the form networks caustics that dominate wave function semiclassical regime following sudden quench. It includes light cone-like propagation correlations as particular case. Caustics are singularities formed by birth and death waves hierarchy universal patterns whose natural mathematical description is via catastrophe theory. Examples classical range from rainbows gravitational lensing optics to tidal bores rogue hydrodynamics. Quantum discretized second quantization (``quantum catastrophes'') live Fock space, which can potentially have many dimensions. illustrate these ideas using Bose Hubbard dimer trimer models, simple enough caustic structure be elucidated first principles yet run full integrable nonintegrable dynamics. The gives rise versions fold cusp catastrophes whereas allows for higher including codimension-3 hyperbolic elliptic umbilics, organized by, projections of, an 8-dimensional corank-2 known ${X}_{9}$. These results hitherto unrecognized universality dynamics manifest strong fluctuations mode population probabilities.