Comparison between formulae for the counting functions of the heights tn of the Riemann
zeros and of semiclassical quantum eigenvalues En suggests that the tn are eigenvalues of …

Multifractal dimensions allow for characterizing the localization properties of states in
complex quantum systems. For ergodic states the finite-size versions of fractal dimensions …

We demonstrate that quantum dynamical localization in the Arnold web of higher-
dimensional Hamiltonian systems is destroyed by an intrinsic classical drift. Thus quantum …

The emergence of random matrix spectral correlations in interacting quantum systems is a
defining feature of quantum chaos. We study such correlations in terms of the spectral form …

For generic 4D symplectic maps we propose the use of 3D phase-space slices, which allow
for the global visualization of the geometrical organization and coexistence of regular and …

In this contribution we will review the basic mathematical aspects of quantum maps. Here is
a brief outline of the topics covered in this contribution. Most of the material comes from …

We derive universal entanglement entropy and Schmidt eigenvalue behaviors for the
eigenstates of two quantum chaotic systems coupled with a weak interaction. The …

Partial transport barriers in the chaotic sea of Hamiltonian systems restrict classical chaotic
transport, as they only allow for a small flux Φ between phase-space regions. In two …

We review the fictitious integrable system approach which predicts dynamical tunneling
rates from regular states to the chaotic region in systems with a mixed phase space. It is …

A transform between functions in and functions in is used to define the analogue of number
and coherent states in the context of finite d-dimensional quantum systems. The coherent …