Searcharxiv⌕ Search

SEARCH · Searcharxiv

Results for “chao-dyn”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5Linked to original sources
arXiv1997

Ergodic Properties of Microcanonical Observables

The problem of the existence of a Strong Stochasticity Threshold in the FPU-beta model is reconsidered, using suitable microcanonical observables of thermodynamic nature, like the temperature and the specific heat. Explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry. Measurements of the corresponding temporal autocorrelation functions locate the threshold at a finite value of the energy density, that results to be indipendent of the number of degrees of freedom.

chao-dyn↗
arXiv1997

Fuzzy phase transition in a 1D coupled stable-map lattice

A coupled-map lattice showing complex behavior in presence of a fully negative Lyapunov spectrum is considered. A phase transition from ordered to disordered evolution upon changing diffusive coupling is studied in detail. Various indicators provide a coherent description of the scenario: the existence of an intermediate transition region characterized by an irregular alternancy of periodic and chaotic evolution.

chao-dyn↗
arXiv1997

Transfer Operators for Coupled Analytic Maps

We consider analytic coupled map lattices over $\Z^d$ with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures with analytic, exponentially bounded finite dimensional marginals. Using residue calculus and `cluster expansion'-like techniques we define transfer operators on these Banach spaces. For these we get a unique probability measure that exhibits exponential decay of correlations.

chao-dyn↗
arXiv1998

Stochastic Responses of the Stable Period-p Orbits in One-Dimensional Noisy Map Systems

We analytically derive the correlation functions of the stochastic response of period-p orbits in a generic one-dimensional map system under the influence of weak external, additive white noise. Two approaches, a recurrence scheme and a path integral method, are provided. Beside the supercycle, we recognise that the fluctuations on each elements of the period-p orbits are colored noise which have non-vanishing time correlation. The results also indicate that the stochastic responses will be stationary after a large number of period-p iterations. The analytical results are confirmed by numerical simulations.

chao-dyn↗
arXiv1998

Coherence, space non-locality and lacunarity in a cascade model of turbulence

We use multiscale-multispace correlations and Fourier transform techniques, to study some intermittent random field properties, which escape analysis by structure function scaling. These properties are parametrized in terms of a set of scale ratios, giving the typical interaction distances in space and scale of the random field fluctuations, and the characteristic lengths over which these fluctuations act coherently to generate intermittency. The relevance of these techniques in turbulence theory is discussed.

chao-dyn↗
arXiv1998

Passive Tracer Dispersion with Random or Periodic Source

In this paper, the author investigates the impact of external sources on the pattern formation and long-time behavior of concentration profiles of passive tracers in a two-dimensional shear flow. It is shown that a time-periodic concentration profile exists for time-periodic external source, while for random source, the distribution functions of all concentration profiles weakly converge to a unique invariant measure (like a stationary state in deterministic systems) as time goes to infinity

chao-dyn↗
arXiv1999

Generalized Stable Multivariate Distribution and Anisotropic Dilations

After having closely re-examined the notion of a Lévy's stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with the help of non isotropic dilations and a related notion of generalized scale. In this framework, the components of a stable vector may not only have distinct Levy's stability indices $α$'s, but the latter may depend on its norm. Indeed, we demonstrate that the Levy's stability index of a vector rather correspond to a linear application than to a scalar, and we show that the former should satisfy a simple spectral property.

chao-dyn↗
arXiv1997

Conductance in a periodically doped quantum wire

In this paper we will give a short rewiew about the conductance of a mesoscopic waveguide strip with a few impurities. Green-function method is used allowing to treat systems with low number of impurities, not only the completly clean case. Investigating a wire containing Dirac-delta potentials (modelling the impurities) we found that increasing number of impurities can cause a transition of the structure of conductance. The staircase like structure of the clean system vanishes and the conductance of a system containing finite number of impurities located periodically will be determined by the band structure of

cond-mat.mes-hall↗
arXiv1999

Random matrices, random polynomials and Coulomb systems

It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special attention devoted to electrostatic analogies. We also discuss the joint probability density of the zeros of polynomials whose coefficients are complex Gaussian variables. This leads to a new two-dimensional solvable gas of interacting particles, with non-trivial interactions between particles.

cond-mat.stat-mech↗
arXiv1996

Application of the diffraction trace formula to the three disk scattering system

The diffraction trace formula ({\em Phys. Rev. Lett.} {\bf 73}, 2304 (1994)) and spectral determinant are tested on the open three disk scattering system. The system contains a generic and exponentially growing number of diffraction periodic orbits. In spite of this it is shown that even the scattering resonances with large imaginary part can be reproduced semiclassicaly. The non-trivial interplay of the diffraction periodic orbits with the usual geometrical orbits produces the fine structure of the complicated spectrum of scattering resonances, which are beyond the resolution of the conventional periodic orbit theory.

chao-dyn↗
arXiv1999

Dissipative Chaotic Quantum Maps: Expectation Values, Correlation Functions and the Invariant State

I investigate the propagator of the Wigner function for a dissipative chaotic quantum map. I show that a small amount of dissipation reduces the propagator of sufficiently smooth Wigner functions to its classical counterpart, the Frobenius-Perron operator, if $\hbar\to 0$. Several consequences arise: The Wigner transform of the invariant density matrix is a smeared out version of the classical strange attractor; time dependent expectation values and correlation functions of observables can be evaluated via hybrid quantum-classical formulae in which the quantum character enters only via the initial Wigner function. If a classical phase-space distribution is chosen for the latter or if the map is iterated sufficiently many times the formulae become entirely classical, and powerful classical trace formulae apply.

chao-dyn↗
arXiv2000

The rate of entropy increase at the edge of chaos

Under certain conditions, the rate of increase of the statistical entropy of a simple, fully chaotic, conservative system is known to be given by a single number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This connection is here generalized to a simple dissipative system, the logistic map, and especially to the chaos threshold of the latter, the edge of chaos. It is found that, in the edge-of-chaos case, the usual Boltzmann-Gibbs-Shannon entropy is not appropriate. Instead, the non-extensive entropy $S_q\equiv \frac{1-\sum_{i=1}^W p_i^q}{q-1}$, must be used. The latter contains a parameter q, the entropic index which must be given a special value $q^*\ne 1$ (for q=1 one recovers the usual entropy) characteristic of the edge-of-chaos under consideration. The same q^* enters also in the description of the sensitivity to initial conditions, as well as in that of the multifractal spectrum of the attractor.

cond-mat.stat-mech↗
arXiv1999

The existence of Burnett coefficients in the periodic Lorentz gas

The linear super-Burnett coefficient gives corrections to the diffusion equation in the form of higher derivatives of the density. Like the diffusion coefficient, it can be expressed in terms of integrals of correlation functions, but involving four different times. The power law decay of correlations in real gases (with many moving particles) and the random Lorentz gas (with one moving particle and fixed scatterers) are expected to cause the super-Burnett coefficient to diverge in most cases. Here we show that the expression for the super-Burnett coefficient of the periodic Lorentz gas converges as a result of exponential decay of correlations and a nontrivial cancellation of divergent contributions.

chao-dyn↗
arXiv1999

Robust and Irreversible Development in Cell Society as a General Consequence of Intra-Inter Dynamics

A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and rules for differentiation are found as a natural consequence of such a system. "Stem cells" that either proliferate or differentiate to different types stochastically are found to appear when intra-cellular dynamics are chaotic. Robustness of the developmental process against microscopic and macroscopic perturbations is shown to be a natural consequence of such intra-inter dynamics, while irreversibility in developmental process is discussed in terms of the gain of stability, loss of diversity and chaotic instability.

chao-dyn↗
arXiv1999

Chaotic dynamics and superdiffusion in a Hamiltonian system with many degrees of freedom

We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when the energy is increased. Strong chaos is found in correspondence to the critical point on top of a weak chaotic regime which characterizes the motion at low energies. For a small region around the critical point, we find anomalous (enhanced) diffusion and Lévy walks in a transient temporal regime before the system relaxes to equilibrium.

cond-mat.stat-mech↗
arXiv1997

Slow modes in passive advection

The anomalous scaling in the Kraichnan model of advection of the passive scalar by a random velocity field with non-smooth spatial behavior is traced down to the presence of slow resonance-type collective modes of the stochastic evolution of fluid trajectories. We show that the slow modes are organized into infinite multiplets of descendants of the primary conserved modes. Their presence is linked to the non-deterministic behavior of the Lagrangian trajectories at high Reynolds numbers caused by the sensitive dependence on initial conditions within the viscous range where the velocity fields are more regular. Revisiting the Kraichnan model with smooth velocities we describe the explicit solution for the stationary state of the scalar. The properties of the probability distribution function of the smeared scalar in this state are related to a quantum mechanical problem involving the Calogero-Sutherland Hamiltonian with a potential.

cond-mat↗
arXiv1996

Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.

gr-qc↗