arXiv subjects

Giampaolo Cristadoro

Publications and source records attributed to Giampaolo Cristadoro.

34 records · Page 2Linked to original sources

arXiv2015

Lévy walks on lattices as multi-state processes

Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of Lévy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times leads to a description of the process in terms of multiple states, whose distributions evolve according to a set of delay differential equations, amenable to analytic treatment. We obtain an exact expression of the mean squared displacement associated with such processes and discuss the emergence of asymptotic scaling laws in regimes of diffusive and superdiffusive (subballistic) transport, emphasizing, in the latter case, the effect of initial conditions on the transport coefficients. Of particular interest is the case of rare ballistic propagation, in which case a regime of superdiffusion may lurk underneath one of normal diffusion.

cond-mat.stat-mech↗

arXiv2014

Transport properties of Lévy walks: an analysis in terms of multistate processes

Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of Lévy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker, we are led to a description of such Lévy walks in terms of multistate processes whose time-evolution is shown to obey a set of coupled delay differential equations. Using simple arguments, we obtain asymptotic solutions to these equations and rederive the scaling laws for the mean squared displacement of such processes. Our calculation includes the computation of all relevant transport coefficients in terms of the parameters of the models.

cond-mat.stat-mech↗

arXiv2014

Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards

We study diffusion on a periodic billiard table with infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a Lévy walk combining exponentially-distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards [Phys. Rev. Lett. 50, 1959 (1983)].

cond-mat.stat-mech↗

arXiv2014

Sparre-Andersen theorem with spatiotemporal correlations

The Sparre-Andersen theorem is a remarkable result in one-dimensional random walk theory concerning the universality of the ubiquitous first-passage-time distribution. It states that the probability distribution $ρ_n$ of the number of steps needed for a walker starting at the origin to land on the positive semi-axes does not depend on the details of the distribution for the jumps of the walker, provided this distribution is symmetric and continuous, where in particular $ρ_n \sim n^{-3/2}$ for large number of steps $n$. On the other hand, there are many physical situations in which the time spent by the walker in doing one step depends on the length of the step and the interest concentrates on the time needed for a return, not on the number of steps. Here we modify the Sparre-Andersen proof to deal with such cases, in rather general situations in which the time variable correlates with the step variable. As an example we present a natural process in 2D that shows deviations from normal scaling are present for the first-passage-time distribution on a semi plane.

cond-mat.stat-mech↗

arXiv2014

Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards

We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of super-diffusion, in the sense that there is a logarithmic correction to the linear growth in time of the mean-squared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time-range accessible to numerical simulations. We compare our simulations to the known analytical results for the variance of the anomalously-rescaled limiting normal distributions.

cond-mat.stat-mech↗

arXiv2013

Follow the fugitive: an application of the method of images to open dynamical systems

Borrowing and extending the method of images we introduce a theoretical framework that greatly simplifies analytical and numerical investigations of the escape rate in open dynamical systems. As an example, we explicitly derive the exact size- and position-dependent escape rate in a Markov case for holes of finite size. Moreover, a general relation between the transfer operators of closed and corresponding open systems, together with the generating function of the probability of return to the hole is derived. This relation is then used to compute the small hole asymptotic behavior, in terms of readily calculable quantities. As an example we derive logarithmic corrections in the second order term. Being valid for Markov systems, our framework can find application in information theory, network theory, quantum Weyl law and via Ulam's method can be used as an approximation method in more general dynamical systems.

nlin.CD↗

arXiv2012

On the origin of long-range correlations in texts

The complexity of human interactions with social and natural phenomena is mirrored in the way we describe our experiences through natural language. In order to retain and convey such a high dimensional information, the statistical properties of our linguistic output has to be highly correlated in time. An example are the robust observations, still largely not understood, of correlations on arbitrary long scales in literary texts. In this paper we explain how long-range correlations flow from highly structured linguistic levels down to the building blocks of a text (words, letters, etc..). By combining calculations and data analysis we show that correlations take form of a bursty sequence of events once we approach the semantically relevant topics of the text. The mechanisms we identify are fairly general and can be equally applied to other hierarchical settings.

physics.data-an↗

arXiv2011

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called `quenched random Lorentz tube'. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

math.DS↗

arXiv2010

Recurrence for quenched random Lorentz tubes

We consider the billiard dynamics in a strip-like set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called `quenched random Lorentz tube'. We prove that, under general conditions, almost every system in the ensemble is recurrent.

math.DS↗

arXiv2008

Statistical properties of intermittent maps with unbounded derivative

We study the ergodic and statistical properties of a class of maps of the circle and of the interval of Lorenz type which present indifferent fixed points and points with unbounded derivative. These maps have been previously investigated in the physics literature. We prove in particular that correlations decay polynomially, and that suitable Limit Theorems (convergence to Stable Laws or Central Limit Theorem) hold for Hölder continuous observables. We moreover show that the return and hitting times are in the limit exponentially distributed.

math.DS↗

arXiv2008

On universality of algebraic decays in Hamiltonian systems

Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincare' recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence of a universal asymptotic decay based on results for a Markov tree model with random scaling factors for the transition probabilities. Numerical simulations for different Hamiltonian systems support this conjecture and permit the determination of the universal exponent.

nlin.CD↗

arXiv2007

Intermittency in two dimensions

We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations, providing analytical and numerical estimates. We study the transport properties of a suitable lift and use a probabilistic argument to derive the full spectrum of transport moments. Finally the dynamical effects of a stochastic perturbation are considered.

nlin.CD↗

arXiv2005

Recycling Parrondo games

We consider a deterministic realization of Parrondo games and use periodic orbit theory to analyze their asymptotic behavior.

nlin.CD↗

arXiv2003

Periodic orbit theory of strongly anomalous transport

We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical appearance of phase transitions in the spectrum of transport exponents is explained.

nlin.CD↗

arXiv2002

Gluon fusion production of the Higgs boson in a Calculable Model with one Extra Dimension

In an extension of the Standard Model with one extra dimension and N=1 supersymmetry compactified on R^1/(Z_2 x Z'_2), we compute the Higgs boson decay width into two gluons, relevant to Higgs production in hadronic collisions. At one loop, the decay width is significantly suppressed with respect to the SM. For a compactification radius 1/R = 370 \pm 70 GeV and a Higgs mass m_H = 127 \pm 8 GeV, as expected in the case of a radiatively generated Fayet-Iliopoulos term, we find it to be less than 15% of the SM result.

hep-ph↗

arXiv2001

Muon anomalous magnetic moment in a Calculable Model with one Extra Dimension

In the framework of a recently proposed extension of the Standard Model, with N=1 SuperSymmetry in 5 dimensions, compactified on R^1/(Z_2 x Z'_2), we compute the muon anomalous magnetic moment at one loop to order (M_W R)^2, where R is the compactification radius. We find the corrections to be small with respect to the SM pure weak contribution and not capable of explaining the present discrepancy between theory and experiment for any sensible value of R.

hep-ph↗