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On the Scott Correction for Relativistic Matter in the Presence of Magnetic Fields

Gonzalo Bley (Aarhus)
Analysis Seminar
Thursday, 19 September, 2019, at 16:15-17:00, in Aud. D3 (1531-215)
We provide a proof of the first correction to the leading asymptotics of the ground-state energy of molecules with pseudo-relativistic electrons in the presence of a magnetic field. This is known as the ``relativistic Scott correction.'' It is shown that neither the leading term nor the Scott correction depends on the magnetic field. Our result extends a previous theorem by Erdös, Fournais, and Solovej to the critical case $\max_k Z_k\alpha = 2/\pi$, where $\alpha$ is the fine structure constant. Therefore, the full range $0 \leq \max_k Z_k\alpha \leq 2/\pi$ is now covered. ($\max_k Z_k\alpha = 0$ corresponds to $\alpha = 0$, which is the non-relativistic case.) Joint work with S. Fournais.
Contact person: Jacob Schach Møller