no. 6
Semiclassics of the quantum current in very strong magnetic fields
[Limite semi-classique du courant quantique en présence d'un champ magnétique très fort]
Fournais, Soren1
1 Université Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay Cedex (France)
Annales de l'Institut Fourier, Tome 52 (2002) no. 6, pp. 1901-1945.

Nous donnons l’asymptotique du courant d’un gaz d’électrons en limite semi-classique dans le régime champ magnétique constant et très fort. Nous supposons très peu de régularité pour le potentiel scalaire V. En particulier, le résultat peut s’appliquer au champ moyen V MTF provenant de la théorie de Thomas-Fermi magnétique. La démonstration repose sur une estimation de la densité d’états au deuxième niveau de Landau.

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.

DOI : 10.5802/aif.1938
Classification : 81V45, 81V70
Keywords: semiclassics, magnetic Thomas-Ferni theory, quantum current
Mot clés : limite semi-classique, théorie magnétique de Thomas-Ferni, courant quantique

Fournais, Soren 1

1 Université Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay Cedex (France) 
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Fournais, Soren. Semiclassics of the quantum current in very strong magnetic fields. Annales de l'Institut Fourier, Tome 52 (2002) no. 6, pp. 1901-1945. doi : 10.5802/aif.1938. https://aif.centre-mersenne.org/articles/10.5802/aif.1938/

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