35 citations · 142 across the 6 of their papers we have counts for
5 papers · 1 filter
Maximal scarring for eigenfunctions of quantum graphs
Gregory Berkolaiko, Brian Winn
We prove the existence of scarred eigenstates for star graphs with scattering matrices at the central vertex which are either a Fourier transform matrix, or a matrix that prohibits…
Localised eigenfunctions in Seba billiards
J. P. Keating, J. Marklof, B. Winn
We describe some new families of quasimodes for the Laplacian perturbed by the addition of a potential formally described by a Dirac delta function. As an application we find, unde…
Relationship between scattering matrix and spectrum of quantum graphs
G. Berkolaiko, B. Winn
We investigate the equivalence between spectral characteristics of the Laplace operator on a metric graph, and the associated unitary scattering operator. We prove that the statist…
No quantum ergodicity for star graphs
G. Berkolaiko, J. P. Keating, B. Winn
We investigate statistical properties of the eigenfunctions of the Schrodinger operator on families of star graphs with incommensurate bond lengths. We show that these eigenfunctio…
Value distribution of the eigenfunctions and spectral determinants of quantum star graphs
J. P. Keating, J. Marklof, B. Winn
We compute the value distributions of the eigenfunctions and spectral determinant of the Schrodinger operator on families of star graphs. The values of the spectral determinant are…