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

We report on some recent striking advances on the quantum unique ergodicity, or QUE
conjecture, concerning the distribution of large frequency eigenfunctions of the Laplacian on …

This is a survey of recent results on quantum ergodicity, specifically on the large energy
limits of matrix elements relative to eigenfunctions of the Laplacian. It is mainly devoted to …

The method of fundamental solutions (MFS) is a popular tool to solve Laplace and
Helmholtz boundary value problems. Its main drawback is that it often leads to ill …

We present an extensive numerical study of spectral statistics and eigenfunctions of
quantized triangular billiards. We compute two million consecutive eigenvalues for six …

We prove that any deterministic matrix is approximately the identity in the eigenbasis of a
large random Wigner matrix with very high probability and with an optimal error inversely …

This is a survey on eigenfunctions of the Laplacian on Riemannian manifolds (mainly
compact and without boundary). We discuss both local results obtained by analyzing …

We consider the wave and Schrödinger equations on a bounded open connected subset of
a Riemannian manifold, with Dirichlet, Neumann or Robin boundary conditions whenever its …

A gas of interacting particles is a paradigmatic example of chaotic systems. It is shown here
that, even if all but one particle are fixed in generic positions, the excited states of the moving …

We report the first large-scale statistical study of very high-lying eigenmodes (quantum
states) of the mushroom billiard proposed by LA Bunimovich [Chaos 11, 802 (2001)]. The …