Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 248

Boundary Conditions for Bulk and Edge States in Quantum Hall Systems

E. Akkermans, J. E. Avron, R. Narevich, R. Seiler

For two dimensional Schr"odinger Hamiltonians we formulate boundary conditions that split the Hilbert space according to the chirality of the eigenstates on the boundary. With magnetic fields, and in particular, for Quantum Hall systems, this splitting corresponds to edge and bulk states. Applications to the integer and fractional Hall effect and some open problems are described.

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