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

Banff International Research Station for Mathematical Innovation and Discovery

We consider two sharp next-order asymptotics problems, namely the asymptotics for the minimum energy for optimal point configurations 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 for inverse power-law interactions with power $\max(0,d-2)\le s<d$, 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 $d-2<s<d$, the two problems have the same minimum. This is based on joint work with Mircea Petrache.

Mathematics; Partial differential equations; Quantum theory; Applied mathematics

video/mp4

Author affiliation: University College London

2019-07-31

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/71156

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/