Importance of Many Particle Correlations to the Collective Debye-Waller Factor in a Single-Particle Activated Dynamic Theory of the Glass Transition.

We theoretically study the importance of many body correlations on the collective Debye-Waller (DW) factor in the context of the Nonlinear Langevin Equation (NLE) single-particle activated dynamics theory of glass transition and its extension to include collective elasticity (ECNLE theory). This microscopic force-based approach envisions structural alpha relaxation as a coupled local-nonlocal process involving correlated local cage and longer range collective barriers. The crucial question addressed here is the importance of the deGennes narrowing contribution versus a literal Vineyard approximation for the collective DW factor that enters the construction of the dynamic free energy in NLE theory. While the Vineyard-deGennes approach-based NLE theory and its ECNLE theory extension yields predictions that agree well with experimental and simulation results, use of a literal Vineyard approximation for the collective DW factor massively overpredicts the activated relaxation time. The current study suggests many particle correlations are crucial for a reliable description of activated dynamics theory of model hard sphere fluids.