LMP Seminar: Where to dig for gold? Simple ‘tricks’ to help find new universality classes

Like categorising atoms into distinct elements by their atomic numbers in the periodic table, one can categorise dynamical systems into distinct universality classes (UCs) by their symmetries and conservation laws. The similarity continues: just like common elements making up most of the materials around us, some common UCs can govern the behaviour of many systems that we encounter every day. For example, the Kardar-Parisi-Zhang UC dictates the scaling behaviour of diverse systems across scales, from nonequilibrium Bose-Einstein condensates to incompressible migratory cell tissues. In this talk, I will describe simple tricks that will help us identify potentially new UCs. These tricks are simple because they only require undergraduate level mathematics to understand. Specifically, these tricks are mean-field, linear stability, linear fluctuating hydrodynamics, and power counter (or zeroth order renormalization group) analyses.