Form factor expansion for large graphs: a diagrammatic approach Academic Article uri icon

abstract

  • The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the periodic orbit sum for a special family of graphs and thus to recover the expression for the form factor predicted by the Random Matrix Theory. The scheme, although producing the expected answer, undercounts orbits of a certain structure, raising doubts about an analogous summation recently proposed for quantum billiards.

published proceedings

  • QUANTUM GRAPHS AND THEIR APPLICATIONS

author list (cited authors)

  • Berkolaiko, G.

citation count

  • 4

complete list of authors

  • Berkolaiko, Gregory

publication date

  • January 2006