A model for colloids: Diffusion dynamics for two-type hard spheres and the associated depletion effect

Zass Alexander, WIAS Berlin

In this talk, we present a physically-motivated model of diffusion dynamics for a system of n hard spheres (colloids) evolving in a bath of infinitely-many very small particles (polymers). We first show that this two-type system with reflection admits a unique strong solution. We then explore the main feature of the model: by projecting the stationary measure onto the subset of the large spheres, these now feel a new attractive short-range dynamical interaction between each other, known in the physics literature as a depletion force, due to the (hidden) small particles. We are able to construct a natural gradient system with depletion interaction, having the projected measure as its stationary measure. Moreover, this dynamics yields, in the high-density limit for the small particles, a constructive dynamical approach to the famous discrete geometry problem of maximising the contact number of n identical spheres. Based on joint work with M. Fradon, J. Kern, and S. Roelly.

Area: CS18 - Interacting systems in statistical physics II (Chiara Franceschini and Elena Magnanini)

Keywords: Stochastic differential equation, Hard-core interaction, Collision Local time, Colloids, Depletion interaction, Gibbs point process

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