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On the current of large atoms in strong magnetic fields

Søren Fournais — 2000

Journées équations aux dérivées partielles

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...

Semiclassics of the quantum current in very strong magnetic fields

Soren Fournais — 2002

Annales de l’institut Fourier

We prove a formula for the current in an electron gas in a semiclassical limit corresponding to strong, constant, magnetic fields. Little regularity is assumed for the scalar potential V . In particular, the result can be applied to the mean field from magnetic Thomas-Fermi theory V MTF . The proof is based on an estimate on the density of states in the second Landau band.

Le troisième champ critique en théorie de Ginzburg-Landau

Søren Fournais

Séminaire Équations aux dérivées partielles

L’objectif de cet exposé est d’étudier la transition de l’état supraconducteur à l’état normal pour un matériau soumis à un champ magnétique. Nous allons donner une démonstration simple et générale de l’équivalence des différentes définitions possibles du champ critique correspondant à cette transition.

Sur le Laplacien magnétique avec condition de Neumann.

Søren Fournais

Séminaire Équations aux dérivées partielles

L’objectif de cet exposé est de décrire de nouveaux résultats (obtenus avec B. Helffer dans []) sur l’asymptotique semiclassique des valeurs propres du Laplacien magnétique sur un domaine dans 2 avec condition de Neumann sur le bord. On discutera aussi l’application de ces résultats à la théorie de Ginzburg-Landau en supraconductivité.

Sharp trace asymptotics for a class of 2 D -magnetic operators

Horia D. CorneanSøren FournaisRupert L. FrankBernard Helffer — 2013

Annales de l’institut Fourier

In this paper we prove a two-term asymptotic formula for the spectral counting function for a 2 D magnetic Schrödinger operator on a domain (with Dirichlet boundary conditions) in a semiclassical limit and with strong magnetic field. By scaling, this is equivalent to a thermodynamic limit of a 2 D Fermi gas submitted to a constant external magnetic field. The original motivation comes from a paper by H. Kunz in which he studied, among other things, the boundary correction for the grand-canonical...

Stability and semiclassics in self-generated fields

László ErdősSoren FournaisJan Philip Solovej — 2013

Journal of the European Mathematical Society

We consider non-interacting particles subject to a fixed external potential V and a self-generated magnetic field B . The total energy includes the field energy β B 2 and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter β tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical...

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