arXiv subjects

Roberto Artuso

Publications and source records attributed to Roberto Artuso.

31 records · Page 2Linked to original sources

arXiv2010

Higher order statistics in the annulus square billiard: transport and polyspectra

Classical transport in a doubly connected polygonal billiard, i.e. the annulus square billiard, is considered. Dynamical properties of the billiard flow with a fixed initial direction are analyzed by means of the moments of arbitrary order of the number of revolutions around the inner square, accumulated by the particles during the evolution. An "anomalous" diffusion is found: the moment of order q exhibits an algebraic growth in time with an exponent different from q/2, like in the normal case. Transport features are related to spectral properties of the system, which are reconstructed by Fourier transforming time correlation functions. An analytic estimate for the growth exponent of integer order moments is derived as a function of the scaling index at zero frequency of the spectral measure, associated to the angle spanned by the particles. The n-th order moment is expressed in terms of a multiple-time correlation function, depending on n-1 time intervals, which is shown to be linked to higher order density spectra (polyspectra), by a generalization of the Wiener-Khincin Theorem. Analytic results are confirmed by numerical simulations.

nlin.CD↗

arXiv2009

Instability statistics and mixing rates

We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of polynomial decay rates of time correlations and Poincaré recurrences in the -quite delicate- case of dynamical systems with weak chaotic properties.

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↗

arXiv2007

Effects of atomic interactions on Quantum Accelerator Modes

We consider the influence of the inclusion of interatomic interactions on the delta-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic transport near quantal resonances. The atomic interaction is modelled by a Gross-Pitaevskii cubic nonlinearity, and we address both attractive (focusing) and repulsive (defocusing) cases. The most remarkable effect is enhancement or damping of the accelerator modes, depending on the sign of the nonlinear parameter. We provide arguments showing that the effect persists beyond mean-field description, and lies within the experimentally accessible parameter range.

nlin.CD↗

arXiv2007

Directed deterministic classical transport: symmetry breaking and beyond

We consider transport properties of a double delta-kicked system, in a regime where all the symmetries (spatial and temporal) that could prevent directed transport are removed. We analytically investigate the (non trivial) behavior of the classical current and diffusion properties and show that the results are in good agreement with numerical computations. The role of dissipation for a meaningful classical ratchet behavior is also discussed.

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↗

arXiv2005

Delocalized and Resonant Quantum Transport in Nonlinear Generalizations of the Kicked Rotor Model

We analyze the effects of a nonlinear cubic perturbation on the delta-Kicked Rotor. We consider two different models, in which the nonlinear term acts either in the position or in the momentum representation. We numerically investigate the modifications induced by the nonlinearity in the quantum transport in both localized and resonant regimes and a comparison between the results for the two models is presented. Analyzing the momentum distributions and the increase of the mean square momentum, we find that the quantum resonances asymptotically are very stable with respect to the nonlinear perturbation of the rotor's phase evolution. For an intermittent time regime, the nonlinearity even enhances the resonant quantum transport, leading to superballistic motion.

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↗

arXiv2003

Cycle expansions for intermittent maps

In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself through intermittency, dynamics where long periods of nearly regular motions are interrupted by irregular chaotic bursts. We discuss the Perron-Frobenius operator formalism for such systems, and show by means of a 1-dimensional intermittent map that intermittency induces branch cuts in dynamical zeta functions. Marginality leads to long-time dynamical correlations, in contrast to the exponentially fast decorrelations of purely chaotic dynamics. We apply the periodic orbit theory to quantitative characterization of the associated power-law decays.

nlin.CD↗

arXiv2003

Effects of a nonlinear perturbation on dynamical tunneling in cold atoms

We perform a numerical analysis of the effects of a nonlinear perturbation on the quantum dynamics of two models describing non-interacting cold atoms in a standing wave of light with a periodical modulated amplitude $A(t)$. One model is the driven pendulum, considered in ref.\cite{raiz1}, and the other is a variant of the well-known Kicked Rotator Model. In absence of the nonlinear perturbation, the system is invariant under some discrete symmetries and quantum dynamical tunnelling between symmetric classical islands is found. The presence of nonlinearity destroys tunnelling, breaking the symmetries of the system. Finally, further consequences of nonlinearity in the kicked rotator case are considered.

nlin.CD↗

arXiv2002

Nonlinearity effects in the kicked oscillator

The quantum kicked oscillator is known to display a remarkable richness of dynamical behaviour, from ballistic spreading to dynamical localization. Here we investigate the effects of a Gross Pitaevskii nonlinearity on quantum motion, and provide evidence that the qualitative features depend strongly on the parameters of the system.

nlin.CD↗

arXiv1996

On the decay of correlations in Sinai billiards with infinite horizon

We compute the decay of the autocorrelation function of the observable $|v_x|$ in the Sinai billiard and of the observable $v_x$ in the associated Lorentz gas with an approximation due to Baladi, Eckmann and Ruelle. We consider the standard configuration where the disks is centered inside a unit square. The asymptotic decay is found to be $C(t) \sim c(R)/t$. An explicit expression is given for the prefactor $c(R)$ as a function of the radius of the scatterer. For the small scatterer case we also present expressions for the preasymptotic regime. Our findings are supported by numerical computations.

chao-dyn↗

arXiv1993

Periodic Orbit Theory of Anomalous Diffusion

We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1-D maps and possible relevance of our findings for more complicated problems is briefly discussed.

chao-dyn↗