Georgia Institute of Technology College of Sciences

This talk is about a random Schroedinger operator describing the dynamics of an electron in a randomly deformed lattice. The periodic displacement configurations which minimize the bottom of the spectrum are characterized. This leads to an amusing problem about minimizing eigenvalues of a Neumann Schroedinger operator with respect to the position of the potential. While this configuration is essentially unique for dimension greater than one, there are infinitely many different minimizing configurations in the one-dimensional case. This is joint work with Jeff Baker, Frederic Klopp, Shu Nakamura and Guenter Stolz.