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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.

Solutions of the Dirac-Fock equations without projector

Éric Paturel (2000)

Journées équations aux dérivées partielles

In this paper we prove the existence of infinitely many solutions of the Dirac-Fock equations with $N$ electrons turning around a nucleus of atomic charge $Z$ , satisfying $N < Z + 1$ and $α max (Z, N) < 2 / (2 / π + π / 2)$ , where $α$ is the fundamental constant of the electromagnetic interaction (approximately 1/137). This work is an improvement of an article of Esteban-Séré, where the same result was proved under more restrictive assumptions on $N$ .

Displaying 1 – 5 of 5

Semiclassics of the quantum current in very strong magnetic fields

Solutions of the Dirac-Fock equations without projector

Spatial patterns for the three species Gross-Pitaevskii system in the plane.

Spectral analysis of relativistic atoms -- interaction with the quantized radiation field.

Stability of matter in classical and quantized fields.

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