Italo Guarneri

Hydrogen atom in monochromatic field: chaos and dynamical photonic localization

The quantum localization phenomenon that strongly limits any quantum process of diffusive ionization that may be started in systems subjected to a periodic perturbation is discussed. 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. It is shown that if the field strength is less than a so-called delocalization border, the distribution over unperturbed levels is exponential in the number of absorbed photons and the corresponding localization length is determined. Using the mapping description, it is shown that the excitation process occurring in a two-dimensional atom proceeds essentially along the same lines as in the one-dimensional model. These predictions are supported by results of numerical simulation, and the possibility of their experimental verification is discussed. >

Quantum resonances and decoherence for δ-kicked atoms

The quantum resonances occurring with δ-kicked atoms when the kicking period is an integer multiple of the half-Talbot time are analysed 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.

Stable quantum resonances in atom optics.

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 Plancks constant, but rather the detuning from the frequency that is resonant in the absence of gravity.

Quantum Fractal Fluctuations

We numerically analyze quantum survival probability fluctuations in an open, classically chaotic system. In a quasiclassical regime and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal pattern, on the grounds of semiclassical arguments. In contrast, we work in a classical regime of complete chaoticity and in a deep quantum regime of strong localization. We provide evidence that fluctuations are still fractal, due to the slow, purely quantum algebraic decay in time produced by dynamical localization. Such findings considerably enlarge the scope of the existing theory.

A Theory for Quantum Accelerator Modes in Atom Optics

Unexpected accelerator modes were recently observed experimentally for cold cesium atoms when driven in the presence of gravity. A detailed theoretical explanation of this quantum effect is presented here. The theory makes use of invariance properties of the system, that are similar to the ones of solids, leading to a separation into independent kicked rotor problems. The analytical solution makes use of an asymptotic approximation very similar to the semiclassical one, except that the small parameter is not Plancks constant, but rather the detuning from the frequency that is resonant in absence of gravity.

Spectral properties and anomalous transport in a polygonal billiard.

We analyze a class of polygonal billiards, whose behavior is conjectured to exhibit a variety of interesting dynamical features. Correlation functions are numerically investigated, and in a subclass of billiard tables they give indications about a singular continuous spectral measure. By lifting billiard dynamics we are also able to study transport properties: the (normal or anomalous) diffusive behavior is theoretically connected to a scaling index of the spectral measure; the proposed identity is shown to agree with numerical simulations. (c) 2000 American Institute of Physics.

Numerical experiments on billiards

We investigate decay properties of correlation functions in a class of chaotic billiards. First we consider the statistics of Poincaré recurrences (induced by a partition of the billiard): the results are in agreement with theoretical bounds by Bunimovich, Sinai, and Bleher, and are consistent with a purely exponential decay of correlations out of marginality. We then turn to the analysis of the velocity-velocity correlation function: except for intermittent situations, the decay is purely exponential, and the decay rates scale in a simple way with the (uniform) curvature of the dispersing arcs. A power-law decay is instead observed when the system is equivalent to an infinite-horizon Lorentz gas. Comments are given on the behaviour of other types of correlation functions, whose decay, during the observed time scale, appears slower than exponential.

Decay of quantum accelerator modes

Experimentally observable quantum accelerator modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable states, analogous to the Wannier-Stark resonances. Different regimes of tunneling, marked by different quantitative dependence of the lifetimes on

Decoherence as a probe of coherent quantum dynamics

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Preliminaries to the ergodic theory of infinite-dimensional systems: A model of radiant cavity

, are identified, depending on the resolution of KAM substructures that is achieved on the scale of