No quantum ergodicity for star graphs Academic Article

abstract

• We investigate statistical properties of the eigenfunctions of the Schrdinger operator on families of star graphs with incommensurate bond lengths. We show that these eigenfunctions are not quantum ergodic in the limit as the number of bonds tends to infinity by finding an observable for which the quantum matrix elements do not converge to the classical average. We further show that for a given fixed graph there are subsequences of eigenfunctions which localise on pairs of bonds. We describe how to construct such subsequences explicitly. These structures are analogous to scars on short unstable periodic orbits. Springer-Verlag 2004.

authors

• Berkolaiko, Gregory

published proceedings

• COMMUNICATIONS IN MATHEMATICAL PHYSICS

author list (cited authors)

• Berkolaiko, G., Keating, J. P., & Winn, B.

citation count

• 31

complete list of authors

• Berkolaiko, G||Keating, JP||Winn, B

publication date

• September 2004

publisher

• Springer Nature  Publisher

published in

• Communications in Mathematical Physics  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4904 Pure Mathematics
• 51 Physical Sciences

Digital Object Identifier (DOI)

• 10.1007/s00220-004-1145-0

start page

• 259

end page

• 285

volume

• 250

issue

• 2

URL

• http://dx.doi.org/10.1007/s00220-004-1145-0