No quantum ergodicity for star graphs
Berkolaiko, G. ; Keating, J. P. ; Winn, B.
arXiv, 0308005 / Harvested from arXiv
Text on arXiv
We investigate statistical properties of the eigenfunctions of the Schrodinger 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 constructions are analogous to scars on short unstable periodic orbits.
Publié le : 2003-08-05
Classification:  Mathematical Physics,  Nonlinear Sciences - Chaotic Dynamics 
@article{0308005,
     author = {Berkolaiko, G. and Keating, J. P. and Winn, B.},
     title = {No quantum ergodicity for star graphs},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0308005}
}

Berkolaiko, G.; Keating, J. P.; Winn, B. No quantum ergodicity for star graphs. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0308005/