We consider the Pauli operator selfadjoint in , . Here , , are the Pauli matrices, is the magnetic potential, is the coupling constant, and is the electric potential which decays at infinity. We suppose that the magnetic field generated by satisfies some regularity conditions; in particular, its norm is lower-bounded by a positive constant, and, in the case , its direction is constant. We investigate the asymptotic behaviour as of the number of the eigenvalues of smaller than , the parameter being fixed. Furthermore, if , we study the asymptotics as of the number of the eigenvalues of situated on the interval with .
On considère l’opérateur de Pauli autoadjoint dans , . Ici , , sont les matrices de Pauli, est le potentiel magnétique, est la constante de couplage, et est le potentiel électrique qui décroît à l’infini. On suppose que le champ magnétique engendré par satisfait à certaines conditions de régularité; en particulier, sa norme est minorée par une constante strictement positive et, dans le cas , sa direction est constante. On analyse le comportement asymptotique quand du nombre des valeurs propres de inférieures à , le paramètre étant fixé. De plus, si , on étudie l’asymptotique lorsque du nombre des valeurs propres de appartenant à l’intervalle avec .
@article{AIF_1999__49_5_1603_0, author = {Raikov, Georgi D.}, title = {Eigenvalue asymptotics for the {Pauli} operator in strong nonconstant magnetic fields}, journal = {Annales de l'Institut Fourier}, pages = {1603--1636}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {49}, number = {5}, year = {1999}, doi = {10.5802/aif.1731}, mrnumber = {2000k:35227}, zbl = {0935.35109}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1731/} }
TY - JOUR AU - Raikov, Georgi D. TI - Eigenvalue asymptotics for the Pauli operator in strong nonconstant magnetic fields JO - Annales de l'Institut Fourier PY - 1999 SP - 1603 EP - 1636 VL - 49 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1731/ DO - 10.5802/aif.1731 LA - en ID - AIF_1999__49_5_1603_0 ER -
%0 Journal Article %A Raikov, Georgi D. %T Eigenvalue asymptotics for the Pauli operator in strong nonconstant magnetic fields %J Annales de l'Institut Fourier %D 1999 %P 1603-1636 %V 49 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1731/ %R 10.5802/aif.1731 %G en %F AIF_1999__49_5_1603_0
Raikov, Georgi D. Eigenvalue asymptotics for the Pauli operator in strong nonconstant magnetic fields. Annales de l'Institut Fourier, Volume 49 (1999) no. 5, pp. 1603-1636. doi : 10.5802/aif.1731. http://archive.numdam.org/articles/10.5802/aif.1731/
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