On the current of large atoms in strong magnetic fields
Journées équations aux dérivées partielles (2000), article no. 4, 14 p.

In this talk I will discuss recent results on the magnetisation/current of large atoms in strong magnetic fields. It is known from the work (E. Lieb, J.P. Solovej, and J. Yngvason, “Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions”, Commun. Math. Phys. (1994), no. 161, 77-124) of Lieb, Solovej and Yngvason that the energy and density of atoms in strong magnetic fields are given to highest order by a Magnetic Thomas Fermi theory (MTF-theory) when the magnetic field strength $B$ and nuclear charge $Z$ satisfy $B{Z}^{-3}\to 0$. It is, however, equally interesting to establish whether MTF-theory also gives the right asymptotic current. In this talk we will prove that this is indeed the case, at least for moderate magnetic fields. However, we will also prove that approximate ground states do not in general give the right asymptotics for the current.

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title = {On the current of large atoms in strong magnetic fields},
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Fournais, Søren. On the current of large atoms in strong magnetic fields. Journées équations aux dérivées partielles (2000), article  no. 4, 14 p. http://www.numdam.org/item/JEDP_2000____A4_0/

[AHS] J. Avron, I. Herbst and B. Simon, Schrödinger operators with magnetic fields. I. General interactions., Duke Math. Journal 45 (1978) No. 4, 847-883. | MR 80k:35054 | Zbl 0399.35029

[ES97] L. Erdös and J. P. Solovej, Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong non-homogeneous magnetic fields. II. Leading order asymptotic estimates, Commun. Math. Phys. 188 ( 1997), 599-656. | Zbl 0909.47052

[Fou00a] S. Fournais, The magnetisation of large atoms in strong magnetic fields, MaPhySto Research Report (2000), no. 14.

[Fou00b] S. Fournais, On the semiclassical asymptotics of the current and magnetisation of a non-interacting electron gas at zero temperature in a strong constant magnetic field, MaPhySto Research Report (2000), no. 13. | Zbl 0986.82006

[LSY94] E. Lieb, J. P. Solovej, and J. Yngvason, Asymptotics of heavy atoms in high magnetic fields : II. Semiclassical regions., Commun. Math. Phys. (1994), no. 161, 77-124. | MR 95f:81103 | Zbl 0807.47058