Theory for Swap Acceleration near the Glass and Jamming Transitions for Continuously Polydisperse Particles

SWAP algorithms can shift the glass transition to lower temperatures, a recent unexplained observation constraining the nature of this phenomenon. Here we show that SWAP dynamics is governed by an effective potential describing both particle interactions as well as their ability to change size. Requiring its stability is more demanding than for the potential energy alone. This result implies that stable configurations appear at lower energies with SWAP dynamics, and thus at lower temperatures when the liquid is cooled. The magnitude of this effect is predicted to be proportional to the width of the radii distribution, and to decrease with compression for finite-range purely repulsive interaction potentials. We test these predictions numerically and discuss the implications of our findings for the glass transition. These results are extended to the case of hard spheres where SWAP is argued to destroy metastable states of the free energy coarse grained on vibrational timescales. Our analysis unravels the soft elastic modes responsible for the speed-up induced by SWAP, and allows us to predict the structure and the vibrational properties of glass configurations reachable with SWAP. In particular, for continuously polydisperse systems we predict the jamming transition to be dramatically altered, as we confirm numerically. A surprising practical outcome of our analysis is a new algorithm that generates ultrastable glasses by a simple descent in an appropriate effective potential.