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At least 919 records · Page 51Linked to original sources
arXiv1995

Universal diffusion near the golden chaos border

We study local diffusion rate $D$ in Chirikov standard map near the critical golden curve. Numerical simulations confirm the predicted exponent $α=5$ for the power law decay of $D$ as approaching the golden curve via principal resonances with period $q_n$ ($D \sim 1/q^α_n$). The universal self-similar structure of diffusion between principal resonances is demonstrated and it is shown that resonances of other type play also an important role.

chao-dyn↗
arXiv1995

Periodic Orbit Quantization beyond Semiclassics

A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher $\hbar$ contributions to the spectral determinant. We apply the theory to billiard systems, and compare the periodic orbit quantization including the first $\hbar$ contribution to the exact quantum mechanical results.

chao-dyn↗
arXiv1996

Critical Behavior of the Sandpile Model as a Self-Organized Branching Process

Kinetic equations, which explicitly take into account the branching nature of sandpile avalanches, are derived. The dynamics of the sandpile model is described by the generating functions of a branching process. Having used the results obtained the renormalization group approach to the critical behavior of the sandpile model is generalized in order to calculate both critical exponents and height probabilities.

cond-mat↗
arXiv1995

Rifts in Spreading Wax Layers

We report experimental results on the rift formation between two freezing wax plates. The plates were pulled apart with constant velocity, while floating on the melt, in a way akin to the tectonic plates of the earth's crust. At slow spreading rates, a rift, initially perpendicular to the spreading direction, was found to be stable, while above a critical spreading rate a "spiky" rift with fracture zones almost parallel to the spreading direction developed. At yet higher spreading rates a second transition from the spiky rift to a zig-zag pattern occurred. In this regime the rift can be characterized by a single angle which was found to be dependent on the spreading rate. We show that the oblique spreading angles agree with a simple geometrical model. The coarsening of the zig-zag pattern over time and the three-dimensional structure of the solidified crust are also discussed.

chao-dyn↗
arXiv1995

The Role of the Environment in Chaotic Quantum Dynamics

We study how the interaction with an external incoherent environment induces a crossover from quantum to classical behavior for a particle whose classical motion is chaotic. Posing the problem in the semiclassical regime, we find that noise produced by the bath coupling rather than dissipation is primarily responsible for the dephasing that results in the ``classicalization'' of the particle. We find that the bath directly alters the phase space structures that signal the onset of classical chaos. This dephasing is shown to have a semiclassical interpretation: the noise renders the interfering paths indistinguishable and therefore incoherent. The noise is also shown to contribute to the quantum inhibition of mixing by creating new paths that interfere coherently.

chao-dyn↗
arXiv1996

Scaling Behavior in Turbulence is Doubly Anomalous

It is shown that the description of anomalous scaling in turbulent systems requires the simultaneous use of two normalization scales. This phenomenon stems from the existence of two independent (infinite) sets of anomalous scaling exponents that appear in leading order, one set due to infrared anomalies, and the other due to ultraviolet anomalies. To expose this clearly we introduce here a set of local fields whose correlation functions depend simultaneously on the the two sets of exponents. Thus the Kolmogorov picture of "inertial range" scaling is shown to fail because of anomalies that are sensitive to the {\em two ends} of this range.

chao-dyn↗
arXiv1996

Addendum: Chaos around a Hénon-Heiles-Inspired Exact Perturbation of a Black Hole

We find that the model of a black hole plus an exterior halo of quadrupoles and octopoles recently proposed by us is more chaotic than previously detected. In fact, the quadrupolar component gives rise also to a chaotic behavior, found after further numerical search. This fact reinforces even more the role of chaos in relativistic core--halo models.

gr-qc↗
arXiv1996

Parametric Correlations of Scattering Phase Shifts and Fluctuations of Delay Times in Few-Channel Chaotic Scattering

By using the supersymmetry method we derive an explicit expression for the parametric correlation function of densities of eigenphases $θ_a$ of the S-matrix in a chaotic quantum system with broken time-reversal symmetry coupled to continua via M equivalent open channels;$\,\,a=1,..,M$ .We use it to find the distribution of derivatives of these eigenphases over the energy ("phaseshift times") as well as over an arbitrary external parameter.We also find the parametric correlations of Wigner-Smith delay times

cond-mat↗
arXiv1996

Order Parameter for the Transition from Phase to Amplitude Turbulence

The maximal conserved phase gradient is introduced as an order parameter to characterize the transition from phase- to defect-turbulence in the complex Ginzburg-Landau equation. It has a finite value in the phase-turbulent regime and decreases to zero when the transition to defect-turbulence is approached. Solutions with a non-zero phase gradient are studied via a Lyapunov analysis. The degree of "chaoticity" decreases for increasing values of the phase gradient and finally leads to stable travelling wave solutions. A modified Kuramoto-Sivashinsky equation for the phase-dynamics is able to reproduce the main features of the stable waves and to explain their origin.

chao-dyn↗
arXiv1996

Lyapunov Exponents from Kinetic Theory for a Dilute, Field-driven Lorentz Gas

Positive and negative Lyapunov exponents for a dilute, random, two-dimensional Lorentz gas in an applied field, $\vec{E}$, in a steady state at constant energy are computed to order $E^{2}$. The results are: $λ_{\pm}=λ_{\pm}^{0}-a_{\pm}(qE/mv)^{2}t_{0}$ where $λ_{\pm}^{0}$ are the exponents for the field-free Lorentz gas, $a_{+}=11/48, a_{-}=7/48$, $t_{0}$ is the mean free time between collisions, $q$ is the charge, $m$ the mass and $v$ is the speed of the particle. The calculation is based on an extended Boltzmann equation in which a radius of curvature, characterizing the separation of two nearby trajectories, is one of the variables in the distribution function. The analytical results are in excellent agreement with computer simulations. These simulations provide additional evidence for logarithmic terms in the density expansion of the diffusion coefficient.

chao-dyn↗
arXiv1996

Can a local repulsive potential trap an electron?

We study the classical dynamics of a charged particle in two dimensions, under the influence of a perpendicular magnetic and an in-plane electric field. We prove the surprising fact that there is a finite region in phase space that corresponds to the otherwise drifting particle being trapped by a local repulsive potential. Our result is a direct consequence of KAM-theory and, in particular, of Moser's theorem. We illustrate it by numerical phase portraits and by an analytic approximation to invariant curves.

chao-dyn↗
arXiv1996

Quasiclassical Random Matrix Theory

We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN unitary matrix, is considered to be a random matrix. Rather than rejecting all knowledge of the system, except for its symmetry, [as with Dyson's circular unitary ensemble], we choose an ensemble which incorporates the knowledge of the shortest periodic orbits, the prime quasiclassical information bearing on the spectrum. The results largely agree with expectations but contain novel features differing from other recent theories.

chao-dyn↗
arXiv1996

Noise Induced Coherence in Neural Networks

We investigate numerically the dynamics of large networks of $N$ globally pulse-coupled integrate and fire neurons in a noise-induced synchronized state. The powerspectrum of an individual element within the network is shown to exhibit in the thermodynamic limit ($N\to \infty$) a broadband peak and an additional delta-function peak that is absent from the powerspectrum of an isolated element. The powerspectrum of the mean output signal only exhibits the delta-function peak. These results are explained analytically in an exactly soluble oscillator model with global phase coupling.

chao-dyn↗
arXiv1996

Scaling of Low-Order Structure Functions in Homogeneous Turbulence

High-resolution direct numerical simulation data for three-dimensional Navier-Stokes turbulence in a periodic box are used to study the scaling behavior of low-order velocity structure functions with positive and negative powers. Similar to high-order statistics, the low-order relative scaling exponents exhibit unambiguous departures from the Kolmogorov 1941 theory and agree well with existing multiscaling models. No transition from normal scaling to anomalous scaling is observed.

chao-dyn↗
arXiv1996

Chaotic properties of quantum many-body systems in the thermodynamic limit

By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction strength drives the system away from integrability. A correspondence with the dynamical chaoticity of an associated $c$-number system is then used to infer properties of the quantum system in the thermodynamic limit.

cond-mat↗
arXiv1996

Field theory of the quantum kicked rotor

The quantum kicked rotor is investigated by field theoretical methods. It is shown that the effective theory describing the long wave length physics of the system is precisely the supersymmetric nonlinear sigma-model for quasi one-dimensional metallic wires. This proves that the analogy between chaotic systems with dynamical localization and disordered metals can indeed be exact. The role of symmetries is discussed.

chao-dyn↗
arXiv1996

Diffusion and localization in chaotic billiards

We study analytically and numerically the classical diffusive process which takes place in a chaotic billiard. This allows to estimate the conditions under which the statistical properties of eigenvalues and eigenfunctions can be described by Random Matrix Theory. In particular the phenomenon of quantum dynamical localization should be observable in real experiments.

cond-mat↗