Uzy Smilansky

Counting nodal domains on surfaces of revolution (2008)

The Exterior-Interior duality expresses a deep connection between the Laplace spectrum in bounded and connected domains in $\mathbb{R}^2$, and the scattering matrices in the exterior of the domains....

Karageorge, Panos D., Smilansky, Uzy

We consider eigenfunctions of the Laplace-Beltrami operator on special surfaces of revolution. For this separable system, the nodal domains of the (real) eigenfunctions form a checker-board pattern,...

y (2007)

Tsampikos Kottos, Uzy Smilansky, Joaquim Fortuny

In this paper we analyze a recent experiment conducted in an anechoic chamber, where the scattering of microwaves from an array of metallic cylinders was measured. This is a system which displays...

Inside-Outside Duality for Planar Billiards - A Numerical Study (2007)

Barbara Dietz, Jean-pierre Eckmann, Claude-Alain Pillet, Uzy Smilansky, Iddo Ussishkin

This paper reports the results of extensive numerical studies related to spectral properties of the Laplacian and the scattering matrix for planar domains (called billiards). There is a close...

Nodal domains on graphs - How to count them and why? (2007)

Band, Ram, Oren, Idan, Smilansky, Uzy

The purpose of the present manuscript is to collect known results and present some new ones relating to nodal domains on graphs, with special emphasize on nodal counts. Several methods for counting...

Quantum chaos on discrete graphs (2007)

The Statistics of the Points Where Nodal Lines Intersect a Reference Curve (2007)

Adapting a method developed for the study of quantum chaos on {\it quantum (metric)} graphs \cite {KS}, spectral $\zeta$ functions and trace formulae for {\it discrete} Laplacians on graphs are...

Aronovitch, Amit, Smilansky, Uzy

We study the intersection points of a fixed planar curve $\Gamma$ with the nodal set of a translationally invariant and isotropic Gaussian random field $\Psi(\bi{r})$ and the zeros of its normal...

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...

Nodal domains on isospectral quantum graphs: the resolution of isospectrality (2006)

Band, Ram, Shapira, Talia, Smilansky, Uzy

We present and discuss isospectral quantum graphs which are not isometric. These graphs are the analogues of the isospectral domains in which were introduced recently in Gordon et al (1992 Bull. Am....

Nodal domains on isospectral quantum graphs: the resolution of isospectrality (2006)

Band, Ram, Shapira, Talia, Smilansky, Uzy

We present and discuss isospectral quantum graphs which are not isometric. These graphs are the analogues of the isospectral domains in which were introduced recently in Gordon et al (1992 Bull. Am....

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...

Nodal domains on isospectral quantum graphs: the resolution of isospectrality ? (2006)

Band, Ram, Shapira, Talia, Smilansky, Uzy

We present and discuss isospectral quantum graphs which are not isometric. These graphs are the analogues of the isospectral domains in R2 which were introduced recently and are all based on Sunada's...

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...

Random discrete Schr\"odinger operators from Random Matrix Theory (2005)

Breuer, Jonathan, Forrester, Peter J., Smilansky, Uzy

We investigate random, discrete Schr\"odiner operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature $\beta$. They...

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...

Irreversible quantum graphs (2003)

Nodal domains on quantum graphs (2003)

Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the...

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....

Magnetic edge states (2002)

Magnetic edge states (2002)

Action Correlations and Random Matrix Theory (2002)

Smilansky, Uzy, Verdene, Basile

The correlations in the spectra of quantum systems are intimately related to correlations which are of genuine classical origin, and which appear in the spectra of actions of the classical periodic...

Quantum Graphs: A simple model for Chaotic Scattering (2002)

Kottos, Tsampikos, Smilansky, Uzy

We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying...

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...

Magnetic edge states (2002)

Spectral cross correlations of magnetic edge states (2002)

Magnetic edge states are responsible for various phenomena of magneto-transport. Their importance is due to the fact that, unlike the bulk of the eigenstates in a magnetic system, they carry electric...

Chaotic Scattering of Microwaves (2001)

We observe strong, non-trivial cross-correlations between the edge states found in the interior and the exterior of magnetic quantum billiards. Our analysis is based on a novel definition of the edge...

Kottos, Tsampikos, Smilansky, Uzy, Fortuny, Joaquim, Nesti, Giuseppe

In this paper we analyze a recent experiment conducted in an anechoic chamber, where the scattering of microwaves from an array of metallic cylinders was measured. This is a system which displays...

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...

Can One Hear the Shape of a Graph? (2001)

Gutkin, Boris, Smilansky, Uzy

We show that the spectrum of the Schrodinger operator on a finite, metric graph determines uniquely the connectivity matrix and the bond lengths, provided that the lengths are non-commensurate and...

Stroboscopic quantization of autonomous systems (2000)

Eckhardt, Bruno, Smilansky, Uzy

We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is...

Combinatorial Identities from the Spectral Theory of Quantum Graphs (2000)

Combinatorial Identities from the Spectral Theory of Quantum Graphs (2000)

We present a few combinatorial identities which were encountered in our work on the spectral theory of quantum graphs. They establish a new connection between the theory of random matrix ensembles...

Holger Schanz, Uzy Smilansky, Professor Aviezri Fraenkel

The purpose of this paper is to present a newly discovered link between three seemingly unrelated subjects—quantum graphs, the theory of random matrix ensembles and combinatorics. We discuss the...

The boundary integral method for magnetic billiards (1999)

Periodic-Orbit Theory of Anderson Localization on Graphs (1999)

We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields...

Trace identities and their semiclassical implications (1999)

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an a-periodic Kronig-Penney model in...

The quantum three-dimensional Sinai billiard - a semiclassical analysis (1999)

The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum...

Spectral Statistics for Quantum Graphs: Periodic Orbits and Combinatorics (1999)

We present a comprehensive semiclassical investigation of the three-dimensional Sinai billiard, addressing a few outstanding problems in "quantum chaos". We were mainly concerned with the accuracy of...

Periodic orbit theory and spectral statistics for quantum graphs (1999)

We consider the Schroedinger operator on graphs and study the spectral statistics of a unitary operator which represents the quantum evolution, or a quantum map on the graph. This operator is the...

Tsampikos Kottos, Uzy Smilansky

We quantize graphs (networks) which consist of a nite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also...

Periodic Orbit Theory and Spectral Statistics for Quantum Graphs (1998)

Kottos, Tsampikos, Smilansky, Uzy

We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We...

Spectral correlations in systems undergoing a transition from periodicity to disorder (1998)

Dittrich, T., Mehlig, B., Schanz, H., Smilansky, Uzy, Pollner, Peter, Vattay, Gabor

We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and...

On the Accuracy of the Semiclassical Trace Formula (1998)

Quantal-Classical Duality and the Semiclassical Trace Formula (1997)

The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit....

Cohen, Doron, Primack, Harel, Smilansky, Uzy

We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum...

Penumbra diffraction in the quantization of concave billiards (1996)

Primack, Harel, Schanz, Holger, Smilansky, Uzy, Ussishkin, Iddo

The semiclassical description of billiard spectra is extended to include the diffractive contributions from orbits which are nearly tangent to a concave part of the boundary. The leading correction...

The Role of Diffraction in the Quantization of Dispersing Billiards (1995)

Primack, Harel, Schanz, Holger, Smilansky, Uzy, Ussishkin, Iddo

We study diffraction corrections to the semiclassical spectral density of dispersing (Sinai) billiards. They modify the contributions of periodic orbits (PO's), with at least one segment which is...

Quantization of Sinai's Billiard - A Scattering Approach (1995)

Semiclassical Quantization of Billiards with Mixed Boundary Conditions (1995)

We obtained the spectrum of the Sinai billiard as the zeroes of a secular equation, which is based on the scattering matrix of a related scattering problem. We show that this quantization method...

Sieber, Martin, Primack, Harel, Smilansky, Uzy, Ussishkin, Iddo, Schanz, Holger

The semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived. The...

Inside-Outside Duality for Planar Billiards -- A Numerical Study (1995)

Dietz, Barbara, Eckmann, Jean-Pierre, Pillet, Claude-Alain, Smilansky, Uzy, Ussishkin, Iddo

This paper reports the results of extensive numerical studies related to spectral properties of the Laplacian and the scattering matrix for planar domains (called billiards). There is a close...

Quantization of the three dimensional Sinai billiard (1995)

Quantal Consequences of Perturbations Which Destroy Structurally Unstable Orbits in Chaotic Billiards (1994)

For the first time a three--dimensional (3D) chaotic billiard -- the 3D Sinai billiard -- was quantized, and high--precision spectra with thousands of eigenvalues were calculated. We present here a...