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.
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 . En particulier, le résultat peut s’appliquer au champ moyen provenant de la théorie de Thomas-Fermi magnétique. La démonstration repose sur une estimation de la densité d’états au deuxième niveau de Landau.
Keywords: semiclassics, magnetic Thomas-Ferni theory, quantum current
Mot clés : limite semi-classique, théorie magnétique de Thomas-Ferni, courant quantique
Fournais, Soren 1
@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}, pages = {1901--1945}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {52}, number = {6}, year = {2002}, doi = {10.5802/aif.1938}, zbl = {1013.81059}, mrnumber = {1954328}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1938/} }
TY - JOUR AU - Fournais, Soren TI - Semiclassics of the quantum current in very strong magnetic fields JO - Annales de l'Institut Fourier PY - 2002 SP - 1901 EP - 1945 VL - 52 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1938/ DO - 10.5802/aif.1938 LA - en ID - AIF_2002__52_6_1901_0 ER -
%0 Journal Article %A Fournais, Soren %T Semiclassics of the quantum current in very strong magnetic fields %J Annales de l'Institut Fourier %D 2002 %P 1901-1945 %V 52 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1938/ %R 10.5802/aif.1938 %G en %F 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/articles/10.5802/aif.1938/
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