Luca Perotti

Quantum suppression of chaotic diffusion: theory and experiment

Abstract In this paper the question whether any limitation of chaos may be expected when considering a highly excited hydrogen atom in an external microwave field is addressed. Comparison between classical and quantum analytical and numerical results is presented. Moreover these results are suitable for direct comparison with laboratory experiments.

Diffusion of a single ion in a one-dimensional optical lattice

We present an experimental study of the spatial diffusion of a single ion in a polarization gradient field. A 24 Mg + ion was radially confined in a two-dimensional radio-frequency (rf) trap, while an optical lattice superimposed to a weak electric potential was applied along the free axis. With the help of a statistical analysis of single ion trajectories, a spatial diffusion constant was obtained as a function of optical potential depth. The results are compared to semiclassical theoretical models for trapped ions and neutral atoms.

Beyond the Fourier Transform: Signal Symmetry Breaking in the Complex Plane

In this letter, we invert the ordinary point of view in the analysis of noisy data by treating the signal as a perturbation of the noise. The generating function of pure noise is represented, in the Complex Plane, by poles and zeros (Froissart doublets) having a universal, isotropic statistical distribution. The presence of a signal breaks this rotational symmetry. This allows to detect signals deeply embedded in noise that traditional methods cannot reach.

Small phase-space structures and their relevance to pulsed quantum evolution: Stepwise ionization of the excited hydrogen atom in a microwave pulse

Experiments have shown that the microwave ionization probability of a highly excited, almost monodimensional, hydrogen atom subjected to a microwave pulse sometimes grows in steps when the peak electric field of the pulse is increased. Classical pulsed simulations display the same steps, which have been traced to phase-space metamorphoses. Quantum numerical calculations again exhibit the same ionization steps. I show that the time sequence of two-level interactions, responsible for the observed steps in the quantum picture, is strictly related to the classical phase-space structures generated by the above-mentioned metamorphoses.

Noise in the complex plane: open problems

In this paper, we present a certain number of computer results that require theoretical support in order to acquire a full status.

Computing high precision Matrix Padé approximants

We describe a new method of computing matrix Padé approximants of series with integer data in an efficient and fraction-free way, by controlling the growth of the size of intermediate coefficients. This algorithm is applied to compute high precision Padé approximants of matrix-valued generating functions of time series. As an illustration we show that we can successfully recover from noisy equidistant sampling data a joint damped signal of four antenna, even in the presence of background signals.

Realistic semiconductor heterostructures design using inverse scattering

We discuss the construction of optimized electronic filters using inverse scattering methods. We study a wide range of densities and temperatures, room temperature included. Discretization methods of the potential (including the self-consistent potential of the conduction electrons) are worked out that retain all its properties.

Extreme value laws for fractal intensity functions in dynamical systems: Minkowski analysis*

Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase--space. In this paper we generalize this situation to fractal landscapes, i.e. intensity functions characterized by an uncountable set of singularities, located on a Cantor set. This reveals the dynamical role of classical quantities like the Minkowski dimension and content, whose definition we extend to account for singular continuous invariant measures. We also introduce the concept of extremely rare event, quantified by non--standard Minkowski constants and we study its consequences to extreme value statistics. Limit laws are derived from formal calculations and are verified by numerical experiments.

Quasi-static Ionization of Rydberg Alkali-metal Atoms: a classical view of the n^(-5) scaling

A fully classical explanation of the nonhydrogenic ionization threshold for low angular momentum Rydberg states of Alkali-metal atoms in a linearly polarized low frequency monochromatic microwave field is given: the classical equivalent to the quantum rate-limiting step, which is responsible for the n^(-5) scaling and which according to the literature initiates what then continues as essentially classical diffusion, is found.

Excited hydrogen atoms in pulsed microwaves: journeys to quantum chaos and back

Abstract Recent “one-dimensional” experiments on hydrogen in microwaves have provided evidence for nonadiabatic transition processes occurring during the rise and fall of a short pulse of strong microwave electric field. Quantum coupling near a level crossing of pairs of quantum eigenstates has been observed to produce transition probabilities exhibiting a classical scaling. Separatrix crossing effects produce near classical, double peaked, experimental final bound state distributions. Some evidence is presented that level crossing and separatrix crossing sometimes can be related. The present system seems useful in the development of the quantum description of near-classical dynamical processes, in terms of the classical character of individual semiclassical eigenstates and the couplings within sets of such states.