Regular and Anomalous Quantum Diffusion in the Fibonacci Kicked Rotator

We study the dynamics of a quantum rotator kicked according to the almost-periodic Fibonacci sequence. A special numerical technique allows us to carry on this investigation for as many as $10^{12}$ kicks. It is shown that above a critical kick strength the excitation of the system is well described by regular diffusion, while below this border it becomes anomalous, and sub-diffusive. A law for the dependence of the exponent of anomalous sub-diffusion on the system parameters is established numerically. The analogy between these results and quantum diffusion in models of quasi-crystal and in the kicked Harper system is discussed.Comment: 7 pages, 4 figures, submitted to Phys. Rev.

Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems

Discretization of phase space usually nullifies chaos in dynamical systems. We show that if randomness is associated with discretization dynamical chaos may survive and be indistinguishable from that of the original chaotic system, when an entropic, coarse-grained analysis is performed. Relevance of this phenomenon to the problem of quantum chaos is discussed.Comment: 4 pages, 4 figure

On conformally recurrent manifolds of dimension greater than 4

Conformally recurrent pseudo-Riemannian manifolds of dimension n>4 are investigated. The Weyl tensor is represented as a Kulkarni-Nomizu product. If the square of the Weyl tensor is nonzero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak's theorem, the explicit expression of the traceless part of the Ricci tensor is obtained, up to a scalar function. The Ricci tensor has at most two distinct eigenvalues, and the recurrence vector is an eigenvector. Lorentzian conformally recurrent manifolds are then considered. If the square of the Weyl tensor is nonzero, the manifold is decomposable. A null recurrence vector makes the Weyl tensor of algebraic type IId or higher in the Bel - Debever - Ortaggio classification, while a time-like recurrence vector makes the Weyl tensor purely electric.Comment: Title changed and typos corrected. 14 page

Multifractal properties of return time statistics

Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets of dimensions is established. Theoretical analysis and numerical examples of dynamical systems in the class of Iterated Functions are presented.Comment: 4 pages, 3 figure

Electron Wave Filters from Inverse Scattering Theory

Semiconductor heterostructures with prescribed energy dependence of the transmittance can be designed by combining: {\em a)} Pad\'e approximant reconstruction of the S-matrix; {\em b)} inverse scattering theory for Schro\"dinger's equation; {\em c)} a unitary transformation which takes into account the variable mass effects. The resultant continuous concentration profile can be digitized into an easily realizable rectangular-wells structure. For illustration, we give the specifications of a 2 narrow band-pass 12 layer $Al_cGa_{1-c}As$ filter with the high energy peak more than {\em twice narrower} than the other.Comment: 4 pages, Revtex with one eps figur

Creating artificial magnetic fields for cold atoms by photon-assisted tunneling

This paper proposes a simple setup for introducing an artificial magnetic field for neutral atoms in 2D optical lattices. This setup is based on the phenomenon of photon-assisted tunneling and involves a low-frequency periodic driving of the optical lattice. This low-frequency driving does not affect the electronic structure of the atom and can be easily realized by the same means which employed to create the lattice. We also address the problem of detecting this effective magnetic field. In particular, we study the center of mass wave-packet dynamics, which is shown to exhibit certain features of cyclotron dynamics of a classical charged particle.Comment: EPL-style, 8 pages, 4 figure

Estimate of a spatially variable reservoir compressibility by assimilation of ground surface displacement data

Abstract. Fluid extraction from producing hydrocarbon reservoirs can cause anthropogenic land subsidence. In this work, a 3-D finite-element (FE) geomechanical model is used to predict the land surface displacements above a gas field where displacement observations are available. An ensemble-based data assimilation (DA) algorithm is implemented that incorporates these observations into the response of the FE geomechanical model, thus re- ducing the uncertainty on the geomechanical parameters of the sedimentary basin embedding the reservoir. The calibration focuses on the uniaxial vertical compressibility c M , which is often the geomechanical parameter to which the model response is most sensitive. The partition of the reservoir into blocks delimited by faults moti- vates the assumption of a heterogeneous spatial distribution of c M within the reservoir. A preliminary synthetic test case is here used to evaluate the effectiveness of the DA algorithm in reducing the parameter uncertainty associated with a heterogeneous c M distribution. A significant improvement in matching the observed data is obtained with respect to the case in which a homogeneous c M is hypothesized. These preliminary results are quite encouraging and call for the application of the procedure to real gas fields

On the statistical distribution of first--return times of balls and cylinders in chaotic systems

We study returns in dynamical systems: when a set of points, initially populating a prescribed region, swarms around phase space according to a deterministic rule of motion, we say that the return of the set occurs at the earliest moment when one of these points comes back to the original region. We describe the statistical distribution of these "first--return times" in various settings: when phase space is composed of sequences of symbols from a finite alphabet (with application for instance to biological problems) and when phase space is a one and a two-dimensional manifold. Specifically, we consider Bernoulli shifts, expanding maps of the interval and linear automorphisms of the two dimensional torus. We derive relations linking these statistics with Renyi entropies and Lyapunov exponents.Comment: submitted to Int. J. Bifurcations and Chao