Anomalous diffusion in the resonant quantum kicked rotor

We study the resonances of the quantum kicked rotor subjected to an excitation that follows a deterministic time-dependent prescription. For the primary resonances we find an analytical relation between the long-time behavior of the standard deviation and the external kick strength. For the secondary resonances we obtain essentially the same result numerically. Selecting the time sequence of the kick allows to obtain a variety of asymptotic wave-function spreadings: super-ballistic, ballistic, sub-ballistic, diffusive, sub-diffusive and localized.Comment: 5 pages, 3 figures To appear in Physica A

Effects of non-local initial conditions in the Quantum Walk on the line

We report an enhancement of the decay rate of the survival probability when non-local initial conditions in position space are considered in the Quantum Walk on the line. It is shown how this interference effect can be understood analytically by using previously derived results. Within a restricted position subspace, the enhanced decay is correlated with a maximum asymptotic entanglement level while the normal decay rate corresponds to initial relative phases associated to a minimum entanglement level.Comment: 5 pages, 1 figure, Elsevier style, to appear in Physica

Quantum walks: decoherence and coin-flipping games

We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first mechanism drives the system towards a classical diffusive behavior. This is used to build new quantum games, similar to the spin-flip game. The second mechanism involves two different possibilities: (a) All the quantum walk links have the same probability of being broken. (b) Only the quantum walk links on a half-line are affected by random breakage. In case (a) the decoherence drives the system to a classical Markov process, whose master equation is equivalent to the dynamical equation of the quantum density matrix. This is not the case in (b) where the asymptotic global chirality distribution unexpectedly maintains some dependence with the initial condition. Explicit analytical equations are obtained for all cases.Comment: 9 pages, 7 figure

Quantum games via search algorithms

We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the two possible states. These games are characterized by a continuous space of strategies and the selection of a particular strategy is determined by the moments when the players measure.Comment: 4 pages, 3 figure

Earthquake scenarios and seismic input for cultural heritage: applications to the cities of Rome and Florence

For historical buildings and monuments, i.e. when considering time intervals of about a million year (we do not want to loose cultural heritage), the applicability of standard estimates of seismic hazard is really questionable. A viable alternative is represented by the use of the scenario earthquakes, characterized at least in terms of magnitude, distance and faulting style, and by the treatment of complex source processes. Scenario-based seismic hazard maps are purely based on geophysical and seismotectonic features of a region and take into account the occurrence frequency of earthquakes only for their classification into exceptional (catastrophic), rare (disastrous), sporadic (very strong), occasional (strong) and frequent. Therefore they may provide an upper bound for the ground motion levels to be expected for most regions of the world, more appropriate than probabilities of exceedance in view of the long time scales required for the protection of historical buildings. The neo-deterministic approach naturally supplies realistic time series of ground motion, which represent also reliable estimates of ground displacement readily applicable to seismic isolation techniques, useful to preserve historical monuments and relevant man made structures. This methodology has been successfully applied to many urban areas worldwide for the purpose of seismic microzoning, to strategic buildings, lifelines and cultural heritage sites; we will discuss its application to the cities of Rome and Florence