Workshop Nosevol #3

Éric Soccorsi : Bulk vs edge in one-edge quantum Hall systems.

We consider a quantum Hall Hamiltonian in a half-plane with Dirichlet boundary conditions along the edge. Quantum states with energy concentration in between two consecutive Landau levels are named edge states. They carry a non-zero current that remains well-localized in a neighborhood of the boundary. On the other hand, states with energies close to a Landau level are referred to as bulk states in the physics literature. Since the magnetic Schrödinger operator under study is invariant with respect to translations along the edge, it is fibered. The asymptotic behavior of the band functions as the wave number goes to infinity reveals that the current carried by a bulk state is small compared to the current carried by an edge state and that the bulk states are small near the edge. This is joint work with P. D. Hislop and N. Popoff.