Geometrical and topological characterization of nodal domains of wave functions and of random waves
Seminar Room 2, Newton Institute Gatehouse
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.