Fish gotta swim, birds gotta fly, I gotta do Feynmann graphs 'til I die: A continuum theory of flocking

Abstract

Flocking - the collective motion of large numbers of organisms or other self-propelled entities - exhibits a number of strange and baffling phenomena. The most baffling is that it exists at all in two dimensions: a long-known theorem of statistical mechanics called the Mermin-Wagner theorem implies that it would be impossible for an arbitrarily large collection of creatures in a 2d plane to all point in the same direction. Yet, apparently, they can all move in the same direction with no difficulty.

In this talk, I'll show that all of these mysteries can be explained by a very general "hydrodynamic" theory of flocks, which summarises the behaviour of ALL flocks in much the same way that the well-known Navier-Stokes equations summarise the behavior of all simple fluids. I`ll then discuss this theory's explanation for the apparent violation of the Mermin-Wagner theorem. In hindsight, this proves to have a simple hand waving explanation, which I'll present.