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We investigate sets of financial non-redundant and nonsynchronously recorded time series. The sets are composed by a number of stock market indices located all over the world in five continents. By properly selecting the time horizon of returns and by using a reference currency we find a meaningful taxonomy. The detection of such a taxonomy proves that interpretable information can be stored in a set of nonsynchronously recorded time series., Comment: 5 pages, 2 figures (4 panels), Revised version Aug 2000

We introduce power-law tail quantum wave packets. We show that they can be seen as eigenfunctions of a Hamiltonian with a physical potential. We prove that the free evolution of these packets presents an asymptotic decay of the maximum of the wave packets which is anomalous for an interval of the characterizing power-law exponent. We also prove that the number of finite moments of the wave packets is a conserved quantity during the evolution of the wave packet in the free space., 5 pages, 3 figures, to appear in Phys. Rev. Lett

We demonstrate that quantum stochastic resonance allows for the noise-controlled synchronization of quantum jumps between the metastable states of the quantized radiation field in a micromaser. Under readily accessible experimental conditions optimal synchronization is achieved at a finite temperature $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}500\mathrm{mK}$ of the environment.

We experimentally detect noise enhanced stability in an unstable physical system. The average escape time from a metastable, periodically driven, system is measured in the stable and unstable regimes in a noisy environment. In the unstable regime, we measure that the average escape time has a maximum for a finite value of the noise intensity. The scaling properties of the average escape time and of the variance of escape times are compared with the predictions obtained for a system in a marginal state.

We investigate the time dependence of the ionization probability of Rydberg atoms driven by microwave fields, both numerically and experimentally. Our exact quantum results provide evidence for an algebraic decay law on suitably chosen time scales, a phenomenon that is considered to be the signature of nonhyperbolic scattering in unbounded classically chaotic motion.

We propose a fast and accurate algorithm generating L\'evy stable stochastic processes of arbitrary index \ensuremath{\alpha} ranging between 0.3 and 1.99. The scale parameter is also controllable. The algorithm is very fast when \ensuremath{\alpha} lies between 0.75 and 1.95.

We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold (a behavior known as the Omori law in geophysics) is consistent with the simultaneous occurrence of (i) a return probability density function characterized by a power law asymptotic behavior and (ii) a power law relaxation decay of its typical scale. Our empirical observation cannot be explained within the framework of simple and widespread stochastic volatility models., 4 pages,4 figures, accepted in PRE