School of Mathematical Sciences

Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Coulomb and Riesz potentials menu

Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Coulomb and Riesz potentials

Speaker: 
Codina Cotar (UCL)
Date/Time: 
Wed, 22/11/2017 - 13:00
Room: 
W316, Queen's Building

We consider two sharp next-order asymptotics problems, namely the asymptotics for the minimum energy for optimal point con figurations and the asymptotics for the many-marginals Optimal Transport, in both cases with Coulomb and Riesz costs with inverse power-law long-range interactions. The first problem describes the ground state of a Coulomb or Riesz gas, while the second appears as a semi-classical limit of the Density Functional Theory energy modelling a quantum version of the same system. Recently the second-order term in these expansions was precisely described, and corresponds respectively to a Jellium and to a Uniform Electron Gas model. The present work shows that for inverse-power-law interactions with power d-2\le s