Semiclassics of the quantum current in very strong magnetic fields
Annales de l'Institut Fourier, Volume 52 (2002) no. 6, p. 1901-1945

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.

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.

DOI : https://doi.org/10.5802/aif.1938
Classification:  81V45,  81V70
Keywords: semiclassics, magnetic Thomas-Ferni theory, quantum current
@article{AIF_2002__52_6_1901_0,
     author = {Fournais, Soren},
     title = {Semiclassics of the quantum current in very strong magnetic fields},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {52},
     number = {6},
     year = {2002},
     pages = {1901-1945},
     doi = {10.5802/aif.1938},
     zbl = {1013.81059},
     mrnumber = {1954328},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2002__52_6_1901_0}
}
Fournais, Soren. Semiclassics of the quantum current in very strong magnetic fields. Annales de l'Institut Fourier, Volume 52 (2002) no. 6, pp. 1901-1945. doi : 10.5802/aif.1938. https://aif.centre-mersenne.org/item/AIF_2002__52_6_1901_0/

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