157 citations · 965 across the 40 of their papers we have counts for
41 papers
Characterization of Chaotic Evolution in Quantum Systems Induced by Random Hermitian Matrices
Arkady Kurnosov, Sven Gnutzmann, Uzy Smilansky
In a recent paper, a semiclassical Lyapunov exponent associated with a quantum Hamiltonian represented by a finite-dimensional Hermitian matrix was defined and placed on a mathemat…
Quantum graph models of quantum chaos: an introduction and some recent applications
Gregory Berkolaiko, Sven Gnutzmann
Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schrödinger Hamiltonians o…
Symmetry Breaking and Phase Transitions in Random Non-Commutative Geometries and Related Random-Matrix Ensembles
Mauro D'Arcangelo, Sven Gnutzmann
Ensembles of random fuzzy non-commutative geometries may be described in terms of finite (\(N^2\)-dimensional) Dirac operators and a probability measure. Dirac operators of type \(…
Information scrambling and chaos induced by a Hermitian Matrix
Sven Gnutzmann, Uzy Smilansky
Given an arbitrary \(V \times V\) Hermitian matrix, considered as a finite discrete quantum Hamiltonian, we use methods from graph and ergodic theories to construct a \textit{quant…
Closed form expressions for the Green's function of a quantum graph -- a scattering approach
Tristan Lawrie, Sven Gnutzmann, Gregor Tanner
In this work we present a three step procedure for generating a closed form expression of the Green's function on both closed and open finite quantum graphs with general self-adjoi…
A trace formula for metric graphs with piecewise constant potentials and multi-mode graphs
Sven Gnutzmann, Uzy Smilansky
We generalize the scattering approach to quantum graphs to quantum graphs with with piecewise constant potentials and multiple excitation modes. The free single-mode case is well-k…