Searching for solutions to the dynamical mean-field theory of glasses by simulating minimally structured glass formers

The glass problem is fundamentally one of dynamics. The recently formulated dynamical mean-field theory (DMFT) of glasses, which is exact in the infinite-dimensional limit d→∞, therefore has the potential to answer several questions about jamming as well as about the non-equilibrium dynamics and rheology of glasses. As yet, however, solutions of the DMFT equations can only be obtained within a narrow range of equilibrium and low-density conditions. Fundamental questions about the nature of jamming and relaxation thus hinge on our understanding of low d systems, which when extrapolated to d→∞, should help distinguish mean-field physics from activated and other non-perturbative processes. Because the rich structure of low-d liquids interferes with such extrapolations, we here turn to two minimally structured glass formers whose descriptions converge to the DMFT in the infinite dimensional limit: the random Lorentz gas (RLG) and hard spheres with the Mari-Kurchan interaction (MK). Surprisingly, extrapolation differences persist between the two models, most notably in the values of the jamming density. Resolving the origin of such discrepancies is essential to understanding the structure of the glass landscape, in particular, and the solutions of the DMFT more generally.