Deterministic single-file dynamics in collisional representation Available to Purchase

We re-examine numerically the diffusion of a deterministic, or ballistic single file with preassigned velocity distribution (Jepsen’s gas) from a collisional viewpoint. For a two-modal velocity distribution, where half the particles have velocity $±c$⁠, the collisional statistics is analytically proven to reproduce the continuous time representation. For a three-modal velocity distribution with equal fractions, where less than $1∕2$ of the particles have velocity $±c$⁠, with the remaining particles at rest, the collisional process is shown to be inhomogeneous; its stationary properties are discussed here by combining exact and phenomenological arguments. Collisional memory effects are then related to the negative power-law tails in the velocity autocorrelation functions, predicted earlier in the continuous time formalism. Numerical and analytical results for Gaussian and four-modal Jepsen’s gases are also reported for the sake of a comparison.