Ultrastable jammed sphere packings with a wide range of particle dispersities

We show that, for a standard continuously polydisperse model with particle-diameter distribution P(σ)∝σ^{-3} and polydispersity index Δ, employing a combination of standard SWAP moves and transient degree of freedom (TDOF) moves during a Lubachevsky-Stillinger-like particle-growth process dramatically increases the generated packings' jamming densities ϕ_{J}(Δ) and coordination numbers Z_{J}(Δ), for a wide range of Δ. The fractional increase in ϕ_{J}(Δ) obtained by employing these moves first increases rapidly with Δ, then plateaus at 6-7% over the range 0.1≲Δ≤0.5; the obtained ϕ_{J} are as high as 0.747 (for Δ=0.50). These density increases are achieved without producing clearly noticeable crystallization or increased fractionation, despite the fact that the packings are quite hyperstatic for all Δ>0. SWAP and TDOF moves also reduce packings' rattler populations by as much as 99% and increase their bulk moduli by as much as 80%.