WIAS Preprint No. 3024, (2023)

Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect


Authors

  • Fradon, Myriam
  • Kern, Julian
    ORCID: 0000-0002-8231-0736
  • Rœlly, Sylvie
  • Zass, Alexander
    ORCID: 0000-0001-6124-842X

2020 Mathematics Subject Classification

  • 60K35 60H10 60J55 82D99

Keywords

  • Stochastic differential equation, hard core interaction, reversible measure, collision local time, colloids, depletion interaction, Gibbs point process

DOI

10.20347/WIAS.PREPRINT.3024

Abstract

We consider a random diffusion dynamics for an infinite system of hard spheres of two different sizes evolving in ℝd, its reversible probability measure, and its projection on the subset of the large spheres. The main feature is the occurrence of an attractive short-range dynamical interaction --- known in the physics literature as a depletion interaction -- between the large spheres, which is induced by the hidden presence of the small ones. By considering the asymptotic limit for such a system when the density of the particles is high, we also obtain a constructive dynamical approach to the famous discrete geometry problem of maximisation of the contact number of n identical spheres in ℝd. As support material, we propose numerical simulations in the form of movies.

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