38 citations · 64 across the 4 of their papers we have counts for
10 papers · 1 filter
Quantum ergodicity on graphs
S. Gnutzmann, J. P. Keating, F. Piotet
We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for lar…
Can one count the shape of a drum?
Sven Gnutzmann, Panos D. Karageorge, Uzy Smilansky
Sequences of nodal counts store information on the geometry (metric) of the domain where the wave equation is considered. To demonstrate this statement, we consider the eigenfuncti…
Spectral correlations of individual quantum graphs
Sven Gnutzmann, Alexander Altland
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional…
Resolving isospectral "drums" by counting nodal domains
Sven Gnutzmann, Uzy Smilansky, Niels Sondergaard
Several types of systems were put forward during the past decades to show that there exist {\it isospectral} systems which are {\it metrically} different. One important class consi…
The morphology of nodal lines-random waves versus percolation
Georg Foltin, Sven Gnutzmann, Uzy Smilansky
In this paper we investigate the properties of nodal structures in random wave fields, and in particular we scrutinize their recently proposed connection with short-range percolati…
Universal spectral statistics in quantum graphs
Sven Gnutzmann, Alexander Altland
We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations…