Cyclic memory in random energy landscapes*

<div style="direction: ltr;">Experiments and simulations had shown that disordered systems subject to cyclic driving reach, after a training phase of multiple cycles, a periodic state which was shown to encode memory. In this state the particle trajectories form closed loops in space which repeat themselves every integer number of periods, thus it can be represented as a limit cycle in the configuration space, or the energy landscape of the system. The high dimensionality of this space renders it impractical to directly simulate dynamics on models of such landscapes, even for simple cases such as Gaussian surfaces. Here we use a novel simulation algorithm, that uses a sampling technique to simulate deterministic forced dynamics on a Gaussian landscape. We show that similarly to amorphous solids, this model undergoes a transition between periodic and a-periodic dynamics at a critical forcing amplitude with similar features to the transition observed in amorphous solids. This indicates that understanding the dynamics on simple models of random energy landscapes can give us valuable insights into the physics of memory retention in amorphous solids and other random materials.</div>