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Isaac Newton Institute for Mathematical Sciences

Geometrical and topological characterization of nodal domains of wave functions and of random waves.

3rd August 2006

Author: Smilansky, U (Weizmann Institute of Science)


We consider wave functions of the Laplacian. Nodal domains display patterns with a large variety of forms and complexity. We studied a few statistical measures which address these forms from geometrical and topological points of view. In some cases, we were able to derive precise expressions for limit distributions which hold in the limit of short wave-lengths.