Graduate Colloquium Winter 2013

January 24, 2013

Arithmetic and quantum chaos on the sphere

Michael Magee
UCSC Mathematics PhD Student

The nodal domains of a real valued function f are the connected components of the complement of the zero locus of f. Blum, Gnutzmann and Smilansky have argued that nodal domain statistics of wavefunctions are an indicator of quantum chaos. Further, using a percolation model, Bogomolny and Schmidt have given precise predictions for these statistics when they arise from chaotic wavefunctions. In this talk, I'll discuss work in progress on the nodal domain statistics of certain 'arithmetic' wavefunctions on the sphere. One can view these results as evidence that these arithmetic wavefunctions are chaotic, despite the classical dynamics on the sphere being integrable.