Memory and rheology: disordered flow in jammed systems

The ability of a disordered material to form memories of its history emerges from the unique properties of different metastable states. Cyclically shearing jammed packings of soft spheres, for example, can lead to an exactly periodic response, with particles returning to the same position at the end of each cycle. This periodicity suggests the existence of local rearrangements that go unstable as the system is sheared forward and then undo themselves as the strain is reversed. Here, we study these complementary rearrangement pairs as the minimal elements of periodic behavior. We search for paired rearrangements using a simple shear algorithm applied to small systems. Although pairs are surprisingly easy to find, we highlight a number of unexpected behaviors with implications for how rearrangements interact as the number of pairs increases.