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Article Dans Une Revue Mathematical Methods in the Applied Sciences Année : 2006

The dressed nonrelativistic electron in a magnetic field

Résumé

We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the $x_{3}$-axis and with a quantized electromagnetic field. When the interaction between the electron and photons is turned off, the electronic system is assumed to have a ground state of finite multiplicity. Because of the translation invariance along the $x_{3}$-axis, we consider the reduced Hamiltonian associated with the total momentum along the $x_{3}$-axis and, after introducing an ultraviolet cutoff and an infrared regularization, we prove that the reduced Hamiltonian has a ground state if the coupling constant and the total momentum along the $x_{3}$-axis are sufficiently small. Finally we determine the absolutely continuous spectrum of the reduced Hamiltonian.

Dates et versions

hal-00008427 , version 1 (05-09-2005)

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Citer

Laurent Amour, Benoît Grébert, Jean-Claude Guillot. The dressed nonrelativistic electron in a magnetic field. Mathematical Methods in the Applied Sciences, 2006, 29 (10), pp.1121-1146. ⟨hal-00008427⟩
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