We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in
bounded Euclidean domains with Dirichlet, Neumann, or Robin boundary condition. We …

Interpreting wave phenomena in terms of an underlying ray dynamics adds a new
dimension to the analysis of linear wave equations. Forming explicit connections between …

Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra
and semiclassical periodic orbit quantization. The method allows one to circumvent the …

Mesoscopic physics has emerged as a new, interdisciplinary field combining concepts of
atomic, molecular, cluster, and condensed-matter physics. On the one hand mesoscopic …

In this article, we present a numerical investigation of three-dimensional electromagnetic
Sinai-like cavities. We computed around 600 eigenmodes for two different geometries: a …

For a large class of quantized ergodic flows the quantum ergodicity theorem states that
almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we …

We give an overview of some new and old results on geometric properties of eigenfunctions
of Laplacians on Riemannian manifolds. We discuss properties of nodal sets and critical …

The quantum unique ergodicity (QUE) conjecture of Rudnick and Sarnak is that every
eigenfunction ϕ n of the Laplacian on a manifold with uniformly hyperbolic geodesic flow …

Semiclassical approximations often involve the use of stationary phase approximations. This
method can be applied when is small in comparison with relevant actions or action …

We study the number of bouncing ball modes in a class of two-dimensional quantized
billiards with two parallel walls. Using an adiabatic approximation we show that …