LMP Seminar: Dynamical Renormalization Group approach to the collective behavior of natural swarms

Biological systems displaying collective behaviour are characterized by strong spatio-temporal correlations, which partly transcend the multiform diversity of their microscopic details, much as it happens in statistical physics systems close to a critical point. The emergence of large-scale patterns from local interactions between the many elements of these biological systems suggests that it is possible to extend the predictive power of theoretical physics to this alley of biology. Moreover, recent experiments show that collective biological systems conform to a hallmark of statistical physics, namely scaling. Scaling laws have been found to be valid both at the static and at the dynamic level, although with critical exponents unlike any known model. An example is represented by natural swarms of insects, whose data unveiled traces of an inertial critical dynamics in the velocities with a dynamical critical exponent z ~ 1.2. To rationalize this evidence, we developed an inertial active field theory in which the velocity is coupled to its generator of internal rotations, namely the spin, through a mode-coupling interaction. Supported by the indication of weak density fluctuations in insect swarms, we study its near-critical regime with a one-loop Renormalization Group approach under the assumption of incompressibility. The presence of friction in the dynamics of the spin rules a paramount crossover between two fixed points: an unstable underdamped fixed point with z =1.3 and a stable overdamped fixed point with z =1.7, where dissipation takes over. We show how finite-size systems with weak dissipation, such as swarms, can actually exhibit the critical dynamics of the unstable fixed point thus achieving a theoretical result which is in fair agreement with experimental data.