# Seminar on mathematical aspects of the quantum Hall effect and related topics

## 23.11.2016      Steve Zelditch (Northwestern University, USA) 16:00 Room: (Joint with QM2 Colloquium) Hörsaal VIII, Hauptgebaude (click to see the map) Title: [pdf] How to fill a domain with quantum states in quantum Hall problems Abstract: Let D be a domain in some surface M. In fact, M could have any dimension. We would like to construct global quantum states on M which are localized in D and completely fill up D without much spillover outside D. We answer the question by making the quantum states eigenstates of a certain Hamiltonian defined so that D is the energy set H < E. The projection onto the corresponding eigenspaces defines a partial Bergman kernel and when normalized properly, it tends to 1 on D and zero outside D as Planck's constant tends to zero. There is a universal transition from 0 to 1.

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