̂H. In mathematics this kind of trace formula was first known as Poisson formula which
gives a relationship between the eigenvalues of the operator d idθ on the circle and the …

The theory of quantum chaos tries to understand how the chaotic behaviour of a classical
Hamiltonian system is reflected in its quantum counterpart. For instance, let M be a compact …

In this paper we construct a sequence of eigenfunctions of the``quantum Arnold's cat
map''that, in the semiclassical limit, shows a strong scarring phenomenon on the periodic …

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 …

Quantum ergodicity for classically chaotic systems has been studied extensively both
theoretically and experimentally in mathematics and physics. Despite this long tradition we …

We consider the quantized hyperbolic automorphisms on the 2-dimensional torus (or
generalized quantum cat maps), and study the localization properties of their eigenstates in …

For a general class of unitary quantum maps, whose underlying classical phase space is
divided into several invariant domains of positive measure, we establish analogues of …

We study the baker's map and its Walsh quantization, as a toy model of a quantized chaotic
system. We focus on localization properties of eigenstates, in the semiclassical régime …

We look at the expectation values for quantized linear symplectic maps on the
multidimensional torus and their distribution in the semiclassical limit. We construct super …

The two archetypal ensembles of random matrices are Wigner real symmetric (Hermitian)
random matrices and Wishart sample covariance real (complex) random matrices. In this …