38 citations · 64 across the 4 of their papers we have counts for
12 papers
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…
On the spectral gap in Andreev graphs
Holger Flechsig, Sven Gnutzmann
We introduce Andreev scattering (electron-hole conversion at an interface of a normal conductor to a superconductor) at the outer vertices of a quantum star graph and examine its e…
Spectra of graphs and semi-conducting polymers
Philipp Schapotschnikow, Sven Gnutzmann
We study the band gap in some semi-conducting polymers with two models: Hückel molecular orbital theory and the so-called free electron model. The two models are directly related t…
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…