Enhanced Long Wavelength Mermin-Wagner Fluctuations in Two-Dimensional Active Crystals and Glasses

Abstract In two-dimensional (2D) systems, the Mermin-Wagner effect plays a significant role, giving rise to striking dimensionality effects marked by long-range density fluctuations and the divergence of various dynamic properties. This effect also unequivocally negates the possibility of stable crystalline phases in 2D particulate systems with continuous degrees of freedom. This effect has been recently discerned in glass-forming liquids, displaying characteristic signatures like the logarithmic divergence of mean squared displacement in the plateau regime. We explored these long-wavelength fluctuations in crystalline solids and glass-forming liquids in the presence of non-equilibrium active forces. Active systems can be thought of as a minimalistic model for understanding various non-equilibrium systems where the constituent particles' dynamics are controlled by both temperature and internal or external active forces. Such models often offer valuable insights into the dynamical behavior of biological systems, such as collections of cells, bacteria, ant colonies, or even synthetic self-propelled Janus colloids. Our study reveals that fluctuations stemming from active forces get strongly coupled with long wavelength fluctuations arising from thermal effects, resulting in dramatic dynamical effects in 2D systems. We also shed light on how these fluctuations impact dynamical heterogeneity, a defining characteristic of glassy dynamics.