Quantum mechanics of chaotic billiards

We study the quantum behaviour of chaotic billiards which exhibit classically diffusive behaviour. In particular we consider the stadium billiard and discuss how the interplay between quantum localization and the rich structure of the classical phase space influences the quantum dynamics. The analysis of this model leads to new insight in the understanding of quantum properties of classically chaotic systems.Comment: 10 pages in RevTex with 8 figures (7 ps-figures attached, color figure 5 (a-d) (in 4 bitmap-files) can be obtained by e-mail request on [email protected]), submitted to Physica

On the foundation of equilibrium quantum statistical mechanics

We discuss the condition for the validity of equilibrium quantum statistical mechanics in the light of recent developments in the understanding of classical and quantum chaotic motion. In particular, the ergodicity parameter is shown to provide the conditions under which quantum statistical distributions can be derived from the quantum dynamics of a classical ergodic Hamiltonian system.Comment: 10 pages (RevTeX), 2 eps figure

Quantum Ergodicity and Localization in Conservative Systems: the Wigner Band Random Matrix Model

First theoretical and numerical results on the global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, in a generic conservative quantum system are presented. In case of quantum localization the eigenfunctions are shown to be typically narrow and solid, with centers randomly scattered within the semicircle energy shell while the Green function spectral density (local spectral density of states) is extended over the whole shell, but sparse.Comment: 4 pages in RevTex and 4 Postscript figures; presented to Phys. Lett.

How complex is the quantum motion?

In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. Here we introduce a notion of complexity for a quantum system and relate it to its stability and reversibility properties.Comment: 4 pages, 3 figures, new figure adde

Measurement and Information Extraction in Complex Dynamics Quantum Computation

We address the problem related to the extraction of the information in the simulation of complex dynamics quantum computation. Here we present an example where important information can be extracted efficiently by means of quantum simulations. We show how to extract efficiently the localization length, the mean square deviation and the system characteristic frequency. We show how this methods work on a dynamical model, the Sawtooth Map, that is characterized by very different dynamical regimes: from near integrable to fully developed chaos; it also exhibits quantum dynamical localization.Comment: 8 pages, 4 figures, Proceeding of "First International Workshop DICE2002 - Piombino (Tuscany), (2002)