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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

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

Presented by Codina Cotar, UCL

27 November 2017 14:00 in CM221

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<= s= 3, the two problems have the same minimum. For the Coulomb potential in d=3, s=1, our result disproves a conjecture from 2014 of Lewin and Lieb, and shows that, whereas minimizers may be different, the minimum values are equal. Furthermore, provided that the crystallization hypothesis in d = 3 analogous to Abrikosov's conjecture holds, then our result verifies the physicists' conjectured1.4442 lower bound on the famous Lieb-Oxford constant. Our result rigorously confirms the predictions made by the physicists decades ago, regarding the optimal value of the Uniform Electron Gas next-order asymptotic term. This is based on joint works with Mircea Petrache (ETH/Santiago).

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