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...
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 . In particular, the result can be applied to the mean field from
magnetic Thomas-Fermi theory . The proof is based on an estimate on the
density of states in the second Landau band.
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.
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 avec condition de Neumann sur le bord. On discutera aussi l’application de ces résultats à la théorie de Ginzburg-Landau en supraconductivité.
We consider superconductors of Type II near the transition from the ‘bulk superconducting’ to the ‘surface superconducting’ state. We prove a new estimate on the order parameter
in the bulk, i.e. away from the boundary. This solves an open problem posed by Aftalion and Serfaty [AS].
In this paper we prove a two-term asymptotic formula for the spectral counting function for a 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 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...
We consider non-interacting particles subject to a fixed external potential and a self-generated magnetic field . The total energy includes the field energy 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 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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