Choice of diameters in a polydisperse model glassformer: Deterministic or stochastic?

In particle-based computer simulations of polydisperse glassforming systems, the particle diameters σ=σ_{1},⋯,σ_{N} of a system with N particles are chosen with the intention to approximate a desired distribution density f with the corresponding histogram. One method to accomplish this is to draw each diameter randomly and independently from the density f. We refer to this stochastic scheme as model S. Alternatively, one can apply a deterministic method, assigning an appropriate set of N values to the diameters. We refer to this method as model D. We show that, for sample-to-sample fluctuations, especially for the glassy dynamics at low temperatures, it matters whether one chooses model S or model D. Using molecular dynamics computer simulations, we investigate a three-dimensional polydisperse nonadditive soft-sphere system with f(s)∼s^{-3}. The swap Monte Carlo method is employed to obtain equilibrated samples at very low temperatures. We show that for model S the sample-to-sample fluctuations due to the quenched disorder imposed by the diameters σ can be explained by an effective packing fraction. Dynamic susceptibilities in model S can be split into two terms: one that is of thermal nature and can be identified with the susceptibility of model D, and another one originating from the disorder in σ. At low temperatures the latter contribution is the dominating term in the dynamic susceptibility. Our study clarifies the pros and cons of the use of models S and D in practice.