Time-Dependent Properties of Sandpiles - Pradhan, Punyabrata (Frontiers in Physics, 2021)
Bak, Tang and Wisenfeld (BTW) proposed the theory of self-oragnized criticality (SOC), and sandpile models, to connect ``1/f'' noise, observed in systems in a diverse natural setting, to the fractal spatial structure. We review some of the existing works on the problem of characterizing time-dependent properties of sandpiles and try to explore if the BTW's original ambition has really been fulfilled. We discuss the exact hydrodynamic structure in a class of conserved stochastic sandpiles, undergoing a nonequilibrium absorbing phase transition. We illustrate how the hydrodynamic framework can be used to capture long-ranged spatio-temporal correlations in terms of large-scale transport and relaxation properties of the systems. We particularly emphasize on certain interesting aspects of sandpiles - the transport instabilities, which emerge through the threshold-activated nature of the dynamics in the systems. We also point out some open issues at the end.