Department of Mathematics

Baylor University

One Bear Place #97328

Waco, TX 76798-7328

USA

office: SDRIC 332C

phone: +1 (254) 710-3723

fax: +1 (254) 710-3569

email: jon_harrison AT baylor.edu

**Research:** Mathematical Physics

I am particularly interested in questions of quantum mechanics on graphs and quantum chaos.

For example, while Bose-Einstein and Fermi-Dirac statistics are the only forms of quantum statistics for indistinguishable particles in three dimensions on a two dimensional surface anyon statistics are also possible. (Anyon statistics appear in the explanation of the fractional quantum Hall effect and have been proposed as a possible architecture for a topological quantum computer.) If the space is further restricted to a one dimensional network (a graph) more new forms of statistics become available determined by the connectivity of the graph. 3-connected graphs behave like Euclidian space with either Bose or Fermi statistics for non-planar graphs and anyon statistics for planar graphs (graphs that can be drawn in the plane without lines crossing). On 2-connected graphs quantum statistics are more complex but independent of the number of particles. While on 1-connected graphs the number of particles as well as the topology of the graph determines the possible statistics.