office: SDRIC 332C
phone: +1 (254) 710-3723
fax: +1 (254) 710-3569
email: jon_harrison AT baylor.edu
Research: Mathematical Physics
I am primarily interested in quantum mechanics on graphs and quantum chaos.
For example, indistinguishable quantum particles restricted to a two dimensional surface can behave as Anyons, rather than the Bosons or Fermions seen in three dimensions. (Anyons appear in the explanation of the fractional quantum Hall effect and have been proposed as a possible architecture for a quantum computer.) If the space the particles live in is restricted further, to a quasi-one-dimensional network (a graph), new forms of Anyon behavior become available determined by the connectivity of the graph. 3-connected graphs behave like Euclidian space with either Bosons or Fermions for non-planar graphs and Anyons for planar graphs (graphs that can be drawn in the plane without edges crossing). On 2-connected graphs the Anyon behavior is more complex but independent of the number of particles. While on 1-connected graphs the number of particles as well as the topology determines the Anyon behavior.