  We show that memory can be encoded in a model amorphous solid subjected to
athermal oscillatory shear deformations, and in an analogous spin model with
disordered interactions, sharing the feature of a deformable energy landscape.
When these systems are subjected to oscillatory shear deformation, they retain
memory of the deformation amplitude imposed in the training phase, when the
amplitude is below a "localization" threshold. Remarkably, multiple,
persistent, memories can be stored using such an athermal, noise-free,
protocol. The possibility of such memory is shown to be linked to the presence
of plastic deformations and associated limit cycles traversed by the system,
which exhibit avalanche statistics also seen in related contexts.
