Transition probabilities and diffusion coefficient in interacting particle systems

Transport processes in dense fluids have been widely studied during the last century. Despite these efforts, a rigorous theory is only available at the small concentration limit (Chapman-Enskog method and Boltzmann equation). A continuous system can be divided into cells small enough to be point-like and large enough to contain many particles (as in deriving hydrodynamic equations, we can consider each cell to be in local equilibrium). A general result for transition rates between neighboring cells, W, has recently been obtained (Di Muro and Hoyuelos PRE 104, 044104, 2021). It gives the dependence of W on the thermodynamic state (interactions are represented by the excess chemical potential). It reproduces Darken's equation (a relationship between the tracer and collective diffusion coefficients, Dc and D, which holds in the absence of memory effects), and predicts that the collective diffusivity does not depend on the thermodynamic state. It also suggests that D/D_0, where D_0 is the tracer diffusivity at low concentration, is a thermodynamic function. These results were verified with molecular dynamics simulations. Furthermore, experimental results for diffusion in solids are consistent with the theory. Its main limitation is that it does not include memory effects. The talk aims to show that, despite this limitation, the theory is able of providing some new insights into an old problem.

Zoom link: https://zoom.us/j/98286706234?pwd=bm1JUFVYcTJkaVl1VU55L0FiWDRIUT09