On the spectral gap in Andreev graphs (2008)
Flechsig, Holger, Gnutzmann, Sven
We introduce Andreev scattering (electron-hole conversion at all interface of a normal conductor to a superconductor) at the outer vertices of a quantum star graph and examine its effect on the...
Spectra of graphs and semi-conducting polymers (2007)
Schapotschnikow, Philipp, Gnutzmann, Sven
We study the band gap in some semi-conducting polymers with two models: H\"uckel molecular orbital theory and the so-called free electron model. The two models are directly related to spectral theory...
On the spectral gap in Andreev graphs (2007)
Flechsig, Holger, Gnutzmann, Sven
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 effect on the...
Geometric characterization of nodal domains: the area-to-perimeter ratio (2006)
Elon, Yehonatan, Gnutzmann, Sven, Joas, Christian, Smilansky, Uzy
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its...
Can one count the shape of a drum? (2006)
Gnutzmann, Sven, Karageorge, Panos D., Smilansky, Uzy
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 eigenfunctions of the...
Can one count the shape of a drum? (2006)
Gnutzmann, Sven, Karageorge, Panos D., Smilansky, Uzy
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 eigenfunctions of the...
Can one count the shape of a drum? (2006)
Gnutzmann, Sven, Karageorge, Panos D., Smilansky, Uzy
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 eigenfunctions of the...
Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics (2006)
Gnutzmann, Sven, Smilansky, Uzy
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 this...
Spectral correlations of individual quantum graphs (2005)
Gnutzmann, Sven, Altland, Alexander
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 a...
Resolving isospectral "drums" by counting nodal domains (2005)
Gnutzmann, Sven, Smilansky, Uzy, Sondergaard, Niels
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 consists of Laplace...
The morphology of nodal lines-random waves versus percolation (2004)
Foltin, Georg, Gnutzmann, Sven, Smilansky, Uzy
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 percolation models. We...
Universal spectral statistics in quantum graphs (2004)
Gnutzmann, Sven, Altland, Alexander
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 to...
Gnutzmann, Sven, Seif, Burkhard
In a series of two papers we investigate the universal spectral statistics of chaotic quantum systems in the ten known symmetry classes of quantum mechanics. In this first paper we focus on the...
Gnutzmann, Sven, Seif, Burkhard
A semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems. The approach is based on periodic...
Nodal domains on quantum graphs (2003)
Gnutzmann, Sven, Smilansky, Uzy, Weber, Joachim
We consider the real eigenfunctions of the Schr\"odinger operator on graphs, and count their nodal domains. The number of nodal domains fluctuates within an interval whose size equals the number of...
Avoided intersections of nodal lines (2002)
Monastra, Alejandro G., Smilansky, Uzy, Gnutzmann, Sven
We consider real eigen-functions of the Schr\"odinger operator in 2-d. The nodal lines of separable systems form a regular grid, and the number of nodal crossings equals the number of nodal domains....
Universal spectral statistics of Andreev billiards: semiclassical approach (2002)
Gnutzmann, Sven, Seif, Burkhard, Von Oppen, Felix, Zirnbauer, Martin R.
The classification of universality classes of random-matrix theory has recently been extended beyond the Wigner-Dyson ensembles. Several of the novel ensembles can be discussed naturally in the...
Klassischer Grenzfall, Semiklassik und Quantenchaos bei kollektiv gekoppelten n-Niveau-Atomen (2002)
Diese Arbeit beschäftigt sich mit der Quantenmechanik und dem klassischen Grenzfall von n-Niveau-Atomen mit kollektiver Wechselwirkung. Der klassische Grenzfall wird erreicht, wenn die Anzahl der...
Nodal domains statistics: a criterion for quantum chaos (2002)
Blum, Galya, Gnutzmann, Sven, Smilansky, Uzy
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 with...
Nodal domains statistics: a criterion for quantum chaos (2002)
Blum, Galya, Gnutzmann, Sven, Smilansky, Uzy
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 with...
Nodal domains statistics - a criterion for quantum chaos (2001)
Blum, Galya, Gnutzmann, Sven, Smilansky, Uzy
We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2-$d$ quantum billiards. We show that these distributions distinguish clearly between systems...
Renyi-Wehrl entropies as measures of localization in phase space (2001)
Gnutzmann, Sven, Zyczkowski, Karol
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 of...
Klassischer Grenzfall, Semiklassik und Quantenchaos bei kollektiv gekoppelten n-Niveau-Atomen (2000)
Diese Arbeit beschäftigt sich mit der Quantenmechanik und dem klassischen Grenzfall von n-Niveau-Atomen mit kollektiver Wechselwirkung. Der klassische Grenzfall wird erreicht, wenn die Anzahl der...
Level Dynamics and Universality of Spectral Fluctuations (2000)
Braun, Peter, Gnutzmann, Sven, Haake, Fritz, Kus, Marek, Zyczkowski, Karol
The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we...