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We study the dynamical localization in a pendulum with slowly modulated amplitude. Because of the phenomenon of separatrix crossing, the classical model shows a diffusive ergodic motion inside a confined phase space region even in the adiabatic limit. We present numerical results on the quantum dynamics which show a gradually increasing localization with decreasing modulation frequency, leading eventually towards quantum adiabaticity in the classical ergodic region.

We discuss the quantum dynamics of the stadium billiard whose classical motion is known to be completely chaotic. In particular, we show how the simultaneous presence of cantori in the classical phase space and of the phenomenon of quantum dynamical localization affects the structure of the eigenfunctions and the statistical properties of the eigenvalues.

By coating a nanotube with a molecular layer that is thicker on one end than the other, it is possible to make a thermal rectifier that allows heat to flow easily along the tube in one direction, but not so easily in the opposite direction.

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., 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 prosen@fiz.uni-lj.si), submitted to Physica D

We present analytical and numerical results for the microwave excitation of nonhydrogenic atoms in a static electric field when up to 1000 photons are required to ionize an atom. For small microwave fields, dynamical localization in photon number leads to exponentially small ionization while above quantum delocalization border ionization goes in a diffusive way. For alkali atoms in a static field the ionization border is much lower than in hydrogen due to internal chaos.

The average shape of the Spectral Local Density of States (LDOS) and eigenfunctions (EFs) has been studied numerically for a conservative dynamical model (three-orbital Lipkin-Meshkov-Glick model) which can exhibit strong chaos in the classical limit. The attention is paid to the comparison of the shape of LDOS with that known for random matrix models, as well as to the shape of the EFs, for different values of the perturbation strength. The classical counterparts of the LDOS has also been studied and found in a remarkable agreement with the quantum calculations. Finally, by making use of a generalization of Brillouin- Wigner perturbation expansion, the form of long tails of LDOS and EFs is given analytically and confirmed numerically., Comment: 12 pages in RevTex and 15 Postscript figures

A quantum dynamical model of two interacting spins, with chaotic and regular components, is investigated using a finite two-particles symmetrized basis. Chaotic eigenstates give rise to an equilibrium occupation number distribution in close agreement with the Bose-Einstein distribution despite the small number of particles ($n=2$). However, the corresponding temperature differs from that derived from the standard Canonical Ensemble. On the other side, an acceptable agreement with the latter is restored by artificially randomizing the model. Different definitions of temperature are then discussed and compared ., Comment: RevteX, 4 pages, 2 figures postscript

We show that dynamical localization for excited hydrogen atoms in magnetic and microwave fields takes place at quite low microwave frequency much lower than the Kepler frequency. The estimates of localization length are given for different parameter regimes, showing that the quantum delocalization border drops significantly as compared to the case of zero magnetic field. This opens up broad possibilities for laboratory investigations., revtex, 11 pages, 3 figures, to appear in Phys. Rev. A, Feb (1997)

We study analytically and numerically the classical diffusive process which takes place in a chaotic billiard. This allows to estimate the conditions under which the statistical properties of eigenvalues and eigenfunctions can be described by Random Matrix Theory. In particular the phenomenon of quantum dynamical localization should be observable in real experiments., 5 latex pages + 5 ps figures, accepted by PRL

In this paper we present an overview of important recent results in the study of a very controversial topic, the so-called quantum chaos. The theoretical and numerical results are compared with real laboratory experiments with special emphasis on the problem of ionization of hydrogen atoms in external microwave fields. (c) 1996 American Institute of Physics.

The model of Fermi particles with random two-body interaction is investigated. This model allows to study the origin and accuracy of statistical laws in few-body systems, the role of interaction and chaos in thermalization, Fermi-Dirac distribution for quasi-particles with spreading widths, matrix elements of external field and enhancement of weak perturbation in chaotic compound states., Comment: 4 pages in RevTex and 2 Postscript figures; to appear in Phys.Rev.E

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., 4 pages in RevTex and 4 Postscript figures; presented to Phys. Lett. A

We investigate the classical dynamics of the helium atom in which one electron is replaced by a heavy particle with a negative charge, such as an antiproton. The general properties of motion and the conditions for chaotic dynamics are studied via the derivation of the planetary map. The regime of strongly correlated motion of two particles is also analyzed. The properties of quantum motion are briefly discussed. {copyright} {ital 1996 The American Physical Society.}

We numerically investigate multiphoton ionization of excited hydrogen atoms in magnetic and microwave fields when up to 600 photons are required for ionization. The analytical estimates for the quantum localization length in the classically chaotic regime are in agreement with numerical data. The excitation is much stronger as compared to the case with microwave field only due to the chaotic structure of eigenstates in magnetic field., Comment: revtex, 9 pages, 3 figures

A Fourier analysis of parametric level dynamics for random matrices periodically depending on a phase is developed. We demonstrate both theoretically and numerically that under very general conditions the correlation $C(\varphi )$ of level velocities is singular at $\varphi =0$ for any symmetry class; the singularity is revealed by algebraic tails in Fourier transforms, and is milder, the stronger the level repulsion in the chosen ensemble. The singularity is strictly connected with the divergence of the 2nd moments of level derivatives of appropriate order, and its type is specified to leading terms for Gaussian, stationary ensembles of GOE, GUE, GSE types, and for the Gaussian ensemble of Periodic Banded Random Matrices, in which a breaking of symmetry occurs. In the latter case, we examine the behaviour of correlations in the diffusive regime and in the localized one as well, finding a singularity like that of pure GUE cases. In all the considered ensembles we study the statistics of the Fourier coefficients of eigenvalues, which are Gaussian distributed for low harmonics, but not for high ones, and the distribution of kinetic energies., Comment: 18 pages, RevTex, 15 figs. available on request from guarneri@mvcomo.fis.unico.it

A Comment on the Letter by Wojciech Hubert Zurek and Juan Pablo Paz, Phys. Rev. Lett. 72, 2508 (1994). The authors of the Letter offer a Reply.