**Universal quantum dynamics: quantum catastrophes** - Duncan O'Dell

Tracking the many-body wave function following a quench in a range of simple systems (e.g. two- and three-site Bose- Hubbard models, particles on a ring, Ising model, Dicke model) reveals certain common structures with characteristic geometric shapes. What are these structures and why do they appear time and again? I will show that they are quantum versions of the catastrophes described by catastrophe theory [1–3]. These quantum catastrophes occur in quantum fields: they are singular in the classical (mean-field) limit and require second-quantization to be well behaved, i.e. the essential discreteness of the excitations of the quantum field needs to be taken into account for a quantum catastrophe to be regularized [4]. They are second quantized versions of more familiar catastrophes such as optical caustics like rainbows and the bright lines on the bottom of swimming pools. Their universality stems from the fact that they are generic (need no symmetry) and structurally stable (immune to perturbations) as guaranteed by catastrophe theory. The fine structure of a quantum catastrophe reveals a network of vortex-antivortex pairs that makes a tantalizing connection to Kibble-Zurek physics.[1] R. Thom, Structural Stability and Morphogenesis (Benjamin, Reading, MA, 1975).[2] V.I. Arnold, Russ. Math. Surv. 30, 1 (1975).[3] M.V. Berry, in Physics of Defects, edited by R. Balian et al., Les Houches, Session XXXV, 1980 (North-Holland Publishing,\r\nAmsterdam, 1981).[4] D.H.J. O’Dell, Phys. Rev. Lett. 109, 150406 (2012).