Permutation symmetry breaking and partial restoration in jammed systems

Disordered solids, such as glasses and jammed packings of athermal particles, have many meta-stable states in a rugged energy landscape.  Starting from random initial particle positions, we enumerate the possible packings of N monodisperse spheres found as the energy is minimized.  If the spheres are indistinguishable, there is permutation symmetry so that any pair of particles can be exchanged.  For small N, some states have a much higher probability to be found than others; for N = 13, we find that some basins are found over 30% of the time. Making the particle distribution polydisperse, even by minute amounts, breaks permutation symmetry and we do not find the same state twice in over 3 x 10⁶ trials. By introducing a new algorithm, we partially restore permutation symmetry into polydisperse packings. The packing energy is minimized while the particle radii are allowed to vary [1]; we then replace the final configuration with the matched set of original radii.  For small polydispersity, the packings found in this way are related to a subset of the monodisperse basins.

[1] V. F. Hagh, et al.  PNAS  119, e21176221