Semiclassics of the quantum current in very strong magnetic fields

Soren Fournais[1]

  • [1] Université Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay Cedex (France)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 6, page 1901-1945
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Fournais, Soren. "Semiclassics of the quantum current in very strong magnetic fields." Annales de l’institut Fourier 52.6 (2002): 1901-1945. <http://eudml.org/doc/116031>.

@article{Fournais2002,
abstract = {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 $V_\{\{\rm MTF\}\}$. The proof is based on an estimate on the density of states in the second Landau band.},
affiliation = {Université Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay Cedex (France)},
author = {Fournais, Soren},
journal = {Annales de l’institut Fourier},
keywords = {semiclassics; magnetic Thomas-Ferni theory; quantum current; electron gas; density of states; second Landau band; hydrogen atoms},
language = {eng},
number = {6},
pages = {1901-1945},
publisher = {Association des Annales de l'Institut Fourier},
title = {Semiclassics of the quantum current in very strong magnetic fields},
url = {http://eudml.org/doc/116031},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Fournais, Soren
TI - Semiclassics of the quantum current in very strong magnetic fields
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 6
SP - 1901
EP - 1945
AB - 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 $V_{{\rm MTF}}$. The proof is based on an estimate on the density of states in the second Landau band.
LA - eng
KW - semiclassics; magnetic Thomas-Ferni theory; quantum current; electron gas; density of states; second Landau band; hydrogen atoms
UR - http://eudml.org/doc/116031
ER -

References

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  13. E. H. Lieb, J. P. Solovej, J. Yngvason, Asymptotics of heavy atoms in high magnetic fields. I. Lowest Landau band regions, Comm. Pure Appl. Math 47 (1994), 513-591 Zbl0800.49041MR1272387
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