Properties of Amorphous Materials Under Periodic Boundary Conditions

A packing with periodic boundary conditions requires that all of the particles' images move in concert. An infinitely repeated structure, on the other hand, has no such constraint. As a consequence, a jammed packing under periodic boundary conditions may have a corresponding infinitely repeated lattice representation that is not jammed, or indeed may not even be at a local minimum. In this manuscript we prove this claim and discuss the ways in which periodic boundary conditions succeed to capture the physics of repeated structures and where they fall short.