Workshop “Mathematical aspects of quantum chaos”
Atelier «Aspects mathématiques du chaos quantique»
June 2-6, 2008/2 au 6 juin 2008
The trace formula for quantum graphs with
general self adoint boundary conditions
Department of Mathematics
Royal Holloway, University of London
Egham, Surrey, TW20 0EX
Quantum graphs are given by self adjoint realisations of Laplacians
(or Dirac- or Pauli-operators) acting on functions on the edges of a com-
pact, metric graph. We study spectral properties of quantum graphs and
prove trace formulae that are closely analogous to Selberg trace formulae.
An important distinction has to be made as to whether the domains of
the operators are characterised by either Robin or non-Robin boundary
conditions in the vertices of the graph.