arXiv subjects

Roberto Artuso

Publications and source records attributed to Roberto Artuso.

At least 19 recordsLinked to original sources

arXiv2026

Stochastically perturbed billiards: fingerprints of chaos and universality classes

Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider the role of a stochastic perturbation of the elastic reflection law, and show that while chaotic billiards maintain their key statistical feature, the behaviour for integrable billiard tables is completely different: it can be linked, for tiny perturbations, to Evans stochastic billiard, where at each collision the reflected angle is a uniformly distributed stochastic variable on $(-π/2,π/2$). The resulting spatial stationary measure has peculiar aspects, like being typically non uniform along the boundary, differently from any chaotic billiard table.

nlin.CD↗

arXiv2024

Exploring run-and-tumble movement in confined settings through simulation

Motion in bounded domains is a fundamental concept in various fields, including billiard dynamics and random walks on finite lattices, with important applications in physics, ecology and biology. An important universal property related to the average return time to the boundary, the Mean Path Length Theorem (MPLT), has been proposed theoretically and confirmed experimentally in various contexts. In this discussion, we investigate a wide range of mechanisms that lead to deviations from this universal behavior, such as boundary effects, reorientation and memory processes. In particular, this study investigates the dynamics of run-and-tumble particles within a confined two-dimensional circular domain. Through a combination of theoretical approaches and numerical simulations, we validate the MPLT under uniform and isotropic particle inflow conditions. The research demonstrates that although the MPLT is generally applicable for different step length distributions, deviations occur for non-uniform angular distributions, non-elastic boundary conditions or memory processes. These results underline the crucial influence of boundary interactions and angular dynamics on the behaviour of particles in confined spaces. Our results provide new insights into the geometry and dynamics of motion in confined spaces and contribute to a better understanding of a broad spectrum of phenomena ranging from the motion of bacteria to neutron transport. This type of analysis is crucial in situations where inhomogeneity occurs, such as multiple real-world scenarios within a limited domain. This bridges the gap between theoretical models and practical applications in biological and physical systems since the study of the statistics of movement in confined settings can bring some light in explaining the mobility mechanism of active agents.

cond-mat.stat-mech↗

arXiv2024

Cauchy universality and random billiards

Motion in bounded domains represents a paradigm in several settings: from billiard dynamics, to random walks in a finite lattice, with applications to relevant physical, ecological and biological problems. A remarkable universal property, involving the average of return times to the boundary, has been theoretically proposed, and experimentally verified in quite different contexts. We discuss here mechanisms that lead to violations of universality, induced by boundary effects. We suggest that our analysis should be relevant where non homogeneity appears in the stationary probability distribution in bounded domain.

cond-mat.stat-mech↗

arXiv2023

Records and occupation time statistics for area-preserving maps

A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated to stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for deterministic systems on a non-compact phase space. We consider here two examples of area-preserving maps: the Chirikov-Taylor standard map and the Casati-Prosen triangle map, and we investigate transport properties, records' statistics and occupation time statistics. While the standard map, when a chaotic sea is present, always reproduces results expected for simple random walks, the triangle map -- whose analysis still displays many elusive points -- behaves in a wildly different way, some of the features being compatible with a transient (non conservative) nature of the dynamics.

nlin.CD↗

arXiv2022

Extreme value statistics of positive recurrent centrally biased random walks

We consider the extreme value statistics of centrally-biased random walks with asymptotically-zero drift in the ergodic regime. We fully characterize the asymptotic distribution of the maximum for this class of Markov chains lacking translational invariance, with a particular emphasis on the relation between the time scaling of the expected value of the maximum and the stationary distribution of the process.

cond-mat.stat-mech↗

arXiv2020

A continuous-time random walk extension of the Gillis model

We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic process allows to significantly change local, non-local and transport properties in the presence of heavy-tailed waiting-time distributions lacking the first moment: we provide here exact results concerning hitting times, first-time events, survival probabilities, occupation times, the moments spectrum and the statistics of records. Specifically, normal diffusion gives way to subdiffusion and we are witnessing the breaking of ergodicity. Furthermore we also test our theoretical predictions with numerical simulations.

cond-mat.stat-mech↗

arXiv2020

Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials

Gillis model, introduced more than 60 years ago, is a non-homogeneous random walk with a position dependent drift. Though parsimoniously cited both in the physical and mathematical literature, it provides one of the very few examples of a stochastic system allowing for a number of exact result, although lacking translational invariance. We present old and novel results for such model, which moreover we show represents a discrete version of a diffusive particle in the presence of a logarithmic potential.

cond-mat.stat-mech↗

arXiv2020

Transport properties and ageing for the averaged Lévy-Lorentz gas

We consider a persistent random walk on an inhomogeneous environment where the reflection probability depends only on the distance from the origin. Such an environment is the result of an average over all realizations of disorder of a Lévy-Lorentz (LL) gas. Here we show that this averaged Lévy-Lorentz gas yields nontrivial results even when the related LL gas is trivial. In particular, we investigate its long time transport properties such as the mean square displacement and the statistics of records, as well as the occurrence of ageing phenomena.

cond-mat.stat-mech↗

arXiv2020

Statistics of occupation time and connection to local properties of non-homogeneous random walks

We consider the statistics of occupation times, the number of visits at the origin and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these observables can be characterized by a single parameter, that is connected to a local property of the probability density function (PDF) of the process, viz., the probability of occupying the origin at time $t$, $P(t)$. We test our results for two different models of lattice random walks with spatially inhomogeneous transition probabilities, one of which of non-Markovian nature, and find good agreement with theory. We also show that the distributions depend only on the occupation probability of the origin by comparing them for the two systems: when $P(t)$ show the same long-time behavior, each observable follows indeed the same distribution.

cond-mat.stat-mech↗

arXiv2018

Non-homogeneous persistent random walks and averaged environment for the Lévy-Lorentz gas

We consider transport properties for a non-homogeneous persistent random walk, that may be viewed as a mean-field version of the Lévy-Lorentz gas, namely a 1-d model characterized by a fat polynomial tail of the distribution of scatterers' distance, with parameter $α$. By varying the value of $α$ we have a transition from normal transport to superdiffusion, which we characterize by appropriate continuum limits.

cond-mat.stat-mech↗

arXiv2016

Anomalous dynamics and the choice of Poincaré recurrence-set

We investigate the dependence of Poincaré recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct relation between the shape of a recurrence-set and the values of its return probability distribution in arbitrary phase-space dimensions. Such procedure, which is shown to be quite effective in the detection of tiny regions of regular motion, allows to explain it why similar recurrence-sets have very different distributions and how to modify them in order to enhance their return probabilities. Applied on data, this permits to understand the co-existence of extremely long, transient power-like decays whose anomalous exponent depends on the chosen recurrence-set.

nlin.CD↗

arXiv2016

Correlation decay and large deviations for mixed systems

We consider low--dimensional dynamical systems with a mixed phase space and discuss the typical appearance of slow, polynomial decay of correlations: in particular we emphasize how this mixing rate is related to large deviations properties.

nlin.CD↗

arXiv2015

Extensive numerical investigations on the ergodic properties of two coupled Pomeau-Manneville maps

We present extensive numerical investigations on the ergodic properties of two identical Pomeau-Manneville maps interacting on the unit square through a diffusive linear coupling. The system exhibits anomalous statistics, as expected, but with strong deviations from the single intermittent map: Such differences are characterized by numerical experiments with densities which {\it do not} have singularities in the marginal fixed point, escape and Poincaré recurrence time statistics that share a power-law decay exponent modified by a clear {\it dimensional} scaling, while the rate of phase-space filling and the convergence of ensembles of Lyapunov exponents show a {\it stretched} instead of pure exponential behaviour. In spite of the lack of rigorous results about this system, the dependence on both the intermittency and the coupling parameters appears to be smooth, paving the way for further analytical development. We remark that dynamical exponents appear to be independent of the (nonzero) coupling strength.

nlin.CD↗

arXiv2015

Oseledets' Splitting of Standard-like Maps

For the class of differentiable maps of the plane and, in particular, for standard-like maps (McMillan form), a simple relation is shown between the directions of the local invariant manifolds of a generic point and its contribution to the finite-time Lyapunov exponents (FTLE) of the associated orbit. By computing also the point-wise curvature of the manifolds, we produce a comparative study between local Lyapunov exponent, manifold's curvature and splitting angle between stable/unstable manifolds. Interestingly, the analysis of the Chirikov-Taylor standard map suggests that the positive contributions to the FTLE average mostly come from points of the orbit where the structure of the manifolds is locally hyperbolic: where the manifolds are flat and transversal, the one-step exponent is predominantly positive and large; this behaviour is intended in a purely statistical sense, since it exhibits large deviations. Such phenomenon can be understood by analytic arguments which, as a by-product, also suggest an explicit way to point-wise approximate the splitting.

math-ph↗

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

Oseledets' Splitting in Large Hamiltonian Systems: the HMF Phase Transition

We consider the covariant Lyapunov vectors (CLV) of a high-dimensional Hamiltonian flow in the case of long range potential, namely the Hamiltonian Mean Field (HMF) problem, by studying the behavior of the Lyapunov spectra and the Oseledets' splitting principal angles (the mutual orientation between stable and unstable subspaces) when a phase transition takes place. Motivated by several results connecting the dynamical properties of systems to their Lyapunov exponents and vectors, we first find confirmation of an explicit sensitivity of such quantities to the transition: our main finding is that the mutual orientation between stable and unstable subspaces fluctuates in time around specific constant values. Moreover, the fluctuations statistics are different above and below the critical threshold, and thus intimately connected to the transition. Pictorially, the evolution of the stability subspaces along a reference orbits turns out to happen only through rigid global rotations plus weak internal deformations between the two subspaces; we are not aware of any theoretical explanation for such a non- trivial setting but, through analogies with integrable systems, we provide some little insight on 'how much' the system resembles an integrable one.

nlin.CD↗

arXiv2013

Comment on "Lyapunov statistics and mixing rates for intermittent systems"

In Pires {\it et al.} [Phys. Rev. E 84, 066210 (2011)] intermittent maps are considered, and the tight relationship between correlation decay of smooth observables and large deviations estimates, as for instance employed in Artuso and Manchein [Phys. Rev. E 80, 036210 (2009)], is questioned. We try to clarify the problem, and provide rigorous arguments and an analytic estimate that disprove the objections raised in Pires {\it et al.} [Phys. Rev. E 84, 066210 (2011)] when ergodic systems are considered.

nlin.CD↗

arXiv2012

Estimating hyperbolicity of chaotic bidimensional maps

We apply to bidimensional chaotic maps the numerical method proposed by Ginelli et al. to approximate the associated Oseledets splitting, i.e. the set of linear subspaces spanned by the so called covariant Lyapunov vectors (CLV) and corresponding to the Lyapunov spectrum. These subspaces are the analog of linearized invariant manifolds for non-periodic points, so the angles between them can be used to quantify the degree of hyperbolicity of generic orbits; however, being such splitting non invariant under smooth transformations of phase space, it is interesting to investigate the properties of transversality when coordinates change, e.g. to study it in distinct dynamical systems. To illustrate this issue on the Chirikov-Taylor standard map we compare the probability densities of transversality for two different coordinate systems; these are connected by a linear transformation that deforms splitting angles through phase space, changing also the probability density of almost-zero angles although complete tangencies are in fact invariant. This is completely due to the PDF transformation law and strongly suggests that any statistical inference from such distributions must be generally taken with care.

nlin.CD↗