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The quantum resonances occurring with δ−kicked atoms when the kicking period is an integer multiple of the half-Talbot time are analyzed in detail. Exact results about the momentum distribution at exact resonance are established, both in the case of totally coherent dynamics and in the case when decoherence is induced by Spontaneous Emission. A description of the dynamics when the kicking period is close to, but not exactly at resonance, is derived by means of a quasi-classical approximation where the detuning from exact resonance plays the role of the Planck constant. In this way scaling laws describing the shape of the resonant peaks are obtained. Such analytical results are supported by extensive numerical simulations, and explain some recent surprising experimental observations. PACS numbers: 05.45.Mt,03.65Yz,72.15Rn,42.50Vk Introduction.The present work is devoted to a detailed theoretical analysis of some of the quantum resonances occurring in the δ-kicked rotor, motivated by laboratory results obtained with experimental realizations of that system. Background.The δ-kicked rotor is a paradigm model in quantum chaology, and its theoretical importance is connected with the long-time properties of its evolution. Among these are effects of purely quantum origin such as dynamical localization [1,2,3,4,5,6,7,8] and the quantum resonances [9,10]. Despite compelling numerical evidence, dynamical localization could not be mathematically proven until very recently ‡. The origin and ‡ A proof for the case of sufficiently small kicking strength has been announced by J. Bourgain and S. Jitomirskaya while the present paper was being prepared for publication. § Similarly noise due to Spontaneous Emission affects non-dispersive quantum wave packets formed in highly excited Rydberg atoms [37,38].

We discuss the quantum localization phenomenon that strongly limits any quantum process of diffusive ionization that may be started in systems subjected to a periodic perturbation. In the case of a highly excited hydrogen atom in a monochromatic field, this phenomenon is theoretically analyzed by reducing the dynamics to appropriate mappings. We show that, if the field strength is less than a "delocalization border," the distribution over unperturbed levels is exponential in the number of absorbed photons and we determine the corresponding localization length. Using the mapping description, we show that the excitation process occurring in a two-dimensional atom goes essentially along the same lines as in the one-dimensional model. We support these predictions by results of numerical simulation, and we discuss the possibility of their experimental verification.

A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold cesium atoms when driven in the presence of gravity, and leads to further predictions. The theory makes use of invariance properties of the system allowing for separation into independent kicked rotor problems. The analysis relies on a fictitious classical limit where the small parameter is not Planck's constant, but rather the detuning from the frequency that is resonant in the absence of gravity.

We report results of numerical investigations of the quantum dynamics of a ID system subject to a time-dependent perturbation with three incommensurate frequencies. These results demonstrate a transition from localized to extended states occurring at a critical value of the perturbation parameter. The dependence of the localization length and of the diffusion rate on this parameter near the critical point is analyzed and found to be in agreement with the predictions of renormalization-group theory.

We present a series of numerical and analytical computations on heat conduction for a strongly chaotic system -the Lorentz gas. Heat conduction is characterized by nontrivial features: While the heat conductivity is well defined in the thermodynamic limit, a linear gradient appears only for quite small temperature differences. The key dynamical feature inducing such a behavior is recognized as deterministic diffusion (along transport direction) which is usually associated to full hyperbolicity. [S0031-9007(99)08614-7] PACS numbers: 44.10. + i, 05.20. -y, 05.45. -a

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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. PACS number 05.45.+bOne of the main results in the study of the so-called quantum chaos has been the discovery of quantum dynamical localization as a mesoscopic quasi-classical phenomenon [1]. This phenomenon has been widely studied and confirmed by many researchers for dynamical models described by maps. Contrary to a common belief, maps describe not only time-dependent systems, but also conservative ones (in the form of Poincare' maps). On the other hand, to our knowledge, there are no direct studies of quantum dynamical localization in bounded conservative models; moreover, the appearance of dynamical localization in such systems due to quantum effects is challenged by some researchers. The existence of localization in conservative systems would restrict quantum distributions to smaller regions of phase space than classically allowed, and would therefore introduce significant deviations from ergodicity.We have addressed this problem on the Wigner Band Random Matrix (WBRM) model, which was introduced by Wigner 40 years ago [2] for the description of complex, conservative quantum systems like atomic nuclei. Due to severe mathematical difficulties, the random matrix theory (RMT) immediately turned to the much simpler case of statistically homogeneous (full) matrices, for which impressive theoretical results have been achieved (see, e.g., Refs.[3]). However, full matrices describe local chaotic structures only, and this limitation is often inacceptable, for instance in the case of atoms [4,5].Generally speaking, RMT is a statistical theory of systems with discrete energy (and frequency) spectrum. Since the latter is a typical property of quantum dynamical chaos [6], RMT provides a statistical description of quantum chaos and, what is very important, one which does not involve any coupling to a thermal bath, which is a standard element in most statistical theories. Moreover, a single matrix from a given statistical ensemble represents the typical (generic) dynamical system of a given class, characterized by a few matrix parameters. This makes an important bridge between dynamical and statistical description of quantum chaos.To the extent that Band Random Matrices can be taken as models for generic few-freedoms conservative systems which are classically strongly chaotic (in particular ergodic) on a compact energy surface, the results presented in this Letter provide the first characterization of the properties of quantum chaos in momentum space for quantum systems of this class.We consider real Hamiltonian matrices of a...