466 citations · 2.7k across the 81 of their papers we have counts for
6 papers · 1 filter
Stationary scattering from a nonlinear network
Sven Gnutzmann, Uzy Smilansky, Stanislav Derevyanko
Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We s…
Scattering from isospectral quantum graphs
Ram Band, Adam Sawicki, Uzy Smilansky
Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral g…
Dynamics of nodal points and the nodal count on a family of quantum graphs
Ram Band, Gregory Berkolaiko, Uzy Smilansky
We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs with a Schrödinger-type differential operator). Using tools such as scattering app…
Trace formula for counting nodal domains on the boundaries of chaotic 2D billiards
Amit Aronovitch, Uzy Smilansky
Given a Dirichlet eigenfunction of a 2D quantum billiard, the boundary domain count is the number of intersections of the nodal lines with the boundary. We study the integer sequen…
Level sets percolation on chaotic graphs
Yehonatan Elon, Uzy Smilansky
One of the most surprising discoveries in quantum chaos was that nodal domains of eigenfunctions of quantum-chaotic billiards and maps in the semi-classical limit display critical…
Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (II)
Idan Oren, Uzy Smilansky
Following the derivation of the trace formulae in the first paper in this series, we establish here a connection between the spectral statistics of random regular graphs and the pr…