2 citations · 6 across the 9 of their papers we have counts for
10 papers
Multifractal eigenfunctions for quantum star graphs
Jonathan P. Keating, Henrik Ueberschaer
We prove that the eigenfunctions of quantum star graphs exhibit multifractal self-similar structure in certain specified circumstances. In the semiclassical regime, when the spectr…
Quantitative equidistribution of eigenfunctions for toral Schrödinger operators
Henrik Ueberschaer
We prove a quantum ergodicity theorem in position space for the eigenfunctions of a Schrödinger operator on a rectangular torus for w…
Non-gaussian waves in Seba's billiard
Pär Kurlberg, Henrik Ueberschaer
The Seba billiard, a rectangular torus with a point scatterer, is a popular model to study the transition between integrability and chaos in quantum systems. Whereas such billiards…
Scarred quasimodes on translation surfaces
Omer Friedland, Henrik Ueberschaer
Rational polygonal billiards are one of the key models among the larger class of pseudo-integrable billiards. Their billiard flow may be lifted to the geodesic flow on a translatio…
The quantum Loschmidt echo on flat tori
Gabriel Rivière, Henrik Ueberschaer
The Quantum Loschmidt Echo is a measurement of the sensitivity of a quantum system to perturbations of the Hamiltonian. In the case of the standard 2-torus, we derive some explicit…
Delocalization for random displacement models with Dirac masses
Henrik Ueberschaer
We study a random Schroedinger operator, the Laplacian with random Dirac delta potentials on a torus T^d_L = R^d/LZ^d, in the thermodynamic limit L\to\infty, for dimension d=2. The…
Uniformly distributed eigenfunctions on tori with random impurities
Henrik Ueberschaer
We study a random Schroedinger operator, the Laplacian with N independently uniformly distributed random delta potentials on flat tori T^d_L = R^d/LZ^d, d = 2, 3, where L > 0 is la…
The trace formula for a point scatterer on a hyperbolic surface with one cusp
Henrik Ueberschaer
We prove an exact trace formula for the Laplacian with a delta potential - also known as a point scatterer - on a non-compact hyperbolic surface of finite volume with one cusp. Our…
The trace formula for a point scatterer on a compact hyperbolic surface
Henrik Ueberschaer
An exact trace formula for the perturbation of the Laplacian by a Dirac delta potential on a compact hyperbolic Riemann surface is derived. The formula can be considered an analogu…
The trace formula for singular perturbations of the Laplacian on hyperbolic surfaces
Henrik Ueberschaer
We prove an analogue of Selberg's trace formula for a delta potential on a hyperbolic surface of finite volume. For simplicity we restrict ourselves to surfaces with at most one cu…