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During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of thisâ€¦ (More)

- Galya Blum, Sven Gnutzmann, Uzy Smilansky
- Physical review letters
- 2002

We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2D quantum billiards. We show that these distributions distinguish clearly between systems withâ€¦ (More)

- Sven Gnutzmann, Holger Schanz, Uzy Smilansky
- Physical review letters
- 2013

We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph-its topology. We consider genericâ€¦ (More)

- U. Kuhl, Ruven HÃ¶hmann, H J StÃ¶ckmann, Sven Gnutzmann
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2007

Nodal domains are studied both for real psiR and imaginary part psiI of the wave functions of an open microwave cavity and found to show the same behavior as wave functions in closed billiards. Inâ€¦ (More)

We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values ofâ€¦ (More)

- Sven Gnutzmann, Alexander Altland
- Physical review letters
- 2004

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 with regard toâ€¦ (More)

Several types of systems have been put forward during the past few decades to show that there exist isospectral systems which are metrically different. One important class consists ofâ€¦ (More)

- Sven Gnutzmann, Alexander Altland
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2005

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 average over aâ€¦ (More)

We consider real eigenfunctions of the SchrÃ¶dinger operator in 2D. The nodal lines of separable systems form a regular grid,and the number of nodal crossings equals the number of nodal domains. Inâ€¦ (More)

- Iain Foulger, Sven Gnutzmann, Gregor Tanner
- Physical review letters
- 2014

We present a continuous-time quantum search algorithm on a graphene lattice. This provides the sought-after implementation of an efficient continuous-time quantum search on a two-dimensional lattice.â€¦ (More)