Special Session 16: 

Diffusion in Coulomb environment and a phase transition

Hirofumi Osada
Kyushu University
Japan
Co-Author(s):    
Abstract:
Diffusion in Coulomb environment and a phase transition. Hirofumi Osada (Kyushu University) I talk homogenization of diffusion in two-dimensional Euclidian space in a periodic Coulomb environment. That is, we consider a periodic point process in the plane and the diffusion has the repulsive interaction with the two-dimensional Coulomb potential with inverse temperature $\beta$ to each particle in the periodic point process. We first prove that the diffusion is diffusive with non-degenerated effective diffusion constant $\gamma$. We then remove one particle from the environment and consider the diffusive scaling limit of the diffusion. Then its new effective constant depending on the inverse temperature $\beta$ has a phase transition whose critical point is given explicitly in terms of the original effective diffusion constant $\gamma$ of the periodic homogenization problem. Using this result, we present explicit bounds for the critical point of the self-diffusion matrices of the two-dimensional strict Coulomb interacting Brownian motions with respect to inverse temperature $\beta$.