A classical analogue of Bose-Einstein condensation in active matter
Nonequilibrium statistical physics of dense active matter is a fascinating and rich playground in which a variety of emergent behaviour is observed. A natural consequence of the high density in the system will be that the active elements will strongly interact with each giving rise to enhancement and inhibition in their collective activity. This nonequilibrium interaction should ultimately give rise to a dynamic arrest at sufficiently high densities, which yields a diffusivity edge. This effect has so far been neglected in all contributions in the literature of dense active matter. In my talk, I will show how one can build on the recent surge in developing generalized thermodynamic descriptions for scalar active matter, and formulate a generic theoretical description for a large class of active matter systems, which can be described by a density field, and incorporated the notion of a diffusivity edge for the first time. This is a density threshold beyond which the effective (density-dependent) diffusivity of the system vanishes. The model can be solved exactly for the stationary-state behaviour of the system - which has been the subject of recent intense investigations - despite being highly singular. The exact solution shows a remarkable emergent feature in the system; a dynamical phase transition that is formally equivalent to Bose-Einstein condensation, despite the system being intrinsically classical. I discuss the relevant generalized thermodynamic properties of the system, and demonstrate how signatures of such behaviour can be sought in experiments.
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