We consider an electron gaz subjected to a constant magnetic field of strength b, described by a mean field hamiltonian (Pauli operator), H(h,b) = (-ih∇ + b A)² – bh + V(x). At zero temperature the energy E of the gaz is given as the sum of the negative eigenvalues of the operator (with the convention that the chemical potential is absorbed in V). The current j is defined as the variational derivative j = δE/δA . In this talk we give results on the asymptotics of j in a semiclassical limit where the distance between Landau levels b h is held fixed—or even allowed to be large—as h →0.

Département de Mathématiques, Université Paris-Sud