Unforgettable random walks: forces and displacements distributions in granular systems.*

Granular systems are known to exhibit memory effects characterized by the remembrance of the past states and preparation history, which affect its future evolution. At the same time there exist a consensus that the force distributions of granular systems follow exponential and gamma distributions; a hallmark of the memory independent Brownian motion. Both of these assertions are mutually contradicting. We resolve this incongruity by experimentally and numerically verifying that the forces, as well as translational and rotational displacements of dense granular systems are governed by log-normal and power law distributions; consequence of a history dependent geometrical Brownian motion. We show the latter to be a natural product of contacts that reign between particles.