Numbers of nodal domains in quantum chaotic billiards

Undergrad research project with Prof Alex Barnett.  October 2010.

I am looking for someone to work with me on a numerical research
project in quantum chaos, probably starting in the new year, or next
summer, described below. It's a question that some well-known people
in the field of quantum chaos and number theory consider important,
but that will require some dexterity in figuring out how to make use
of some codes I have written, and gather the data (ie, experience with
C or Matlab, etc).  Anyway, it could make a nice senior thesis, or a
shorter project, that has some good `bang for the buck'. Get in touch
with me if interested.

The highly-excited vibrational modes of a drum (or quantum billiard)
have regions of positive and negative motion that divide the surface
into so-called nodal domains. In the last few years Bogomolny-Schmit
proposed a percolation model which predicts the number and variance of
these domains, but very few tests of this have been done using actual
systems. The project would be to do a large-scale, and possibly
publishable, numerical study of the numbers of nodal domains in
chaotic billiards, and Maass forms. Both are of current interest to
mathematicians---in particular number theorists such as Peter
Sarnak. Codes exist for the modes; you will need to interface to them
for the data collection, so programming experience (eg, C or Matlab)
is essential.

Winter/Spring/Summmer 2011 would be ideal.