Long-lived giant number fluctuations in a nonequilibrium nematic

Density is a property that one can measure with arbitrary accuracy for normal materials simply by increasing the size of the volume observed. This is because a region of volume $V$, with $N$ particles on average, ordinarily shows fluctuations with standard deviation $\Delta N \propto \sqrt{N}$, so that fluctuations in the number density go down as $1/\sqrt{V}$. Liquid-crystalline phases of active or self-propelled particles - herds of cattle, schools of fish, motile cells, filaments driven by motor proteins - are quite another matter, with $\Delta N$ predicted to grow much faster than $\sqrt{N}$, and as fast as $N$ in some cases, making density an ill-defined quantity even in the limit of a large system. Here, we present an experimental test of these ideas, on a vertically vibrated horizontal monolayer of rods. In the nematic phase of this system, we establish the existence of giant number fluctuations, $\Delta N \propto N$, previously seen only in computer simulations by Chate et al. We further show that these number fluctuations are long-lived, decay only logarithmically in time, and can be detected even by studying density fluctuations in small subsystems. This behaviour stands in stark contrast to that of nematic phases in thermal equilibrium or, indeed, to any equilibrium system.