Estimation semi-classique du courant quantique en présence d'un grand champ magnétique variable

Abstract : The Pauli operator describes the energy of an electron submitted to a magnetic field and to an external electric potential. The presence of the magnetic field induces a natural quantity, the current. Formally, the current can be considered as the derivative of the energy with respect to the magnetic potential. In this thesis, we establish an asymptotic formula of the current in the presence of a strong variable magnetic field. In the calulations we use a commutator identity that leads us to estimate the sum of eigenvalues of a modified Pauli operator. The technique of the proof relies on the construction of coherent states (in order to approach the eigenfunctions) and Lieb-Thirring inequalities in order to control the error terms.
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Sourour Negra. Estimation semi-classique du courant quantique en présence d'un grand champ magnétique variable. Mathématiques [math]. Université Paris Sud - Paris XI, 2008. Français. ⟨tel-00286992⟩

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