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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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Steve Zelditch, Northwestern University
Lecture Hall VIII, Main Building
Contact: George Marinescu