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At least 1,189 records · Page 66Linked to original sources
arXiv2000

Quantum transport through ballistic cavities: soft vs. hard quantum chaos

We study transport through a two-dimensional billiard attached to two infinite leads by numerically calculating the Landauer conductance and the Wigner time delay. In the generic case of a mixed phase space we find a power law distribution of resonance widths and a power law dependence of conductance increments apparently reflecting the classical dwell time exponent, in striking difference to the case of a fully chaotic phase space. Surprisingly, these power laws appear on energy scales {\em below} the mean level spacing, in contrast to semiclassical expectations.

cond-mat.mes-hall↗
arXiv1999

Stochastic field theory for a Dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white noise potential, the gauge field disorder. Effective supersymmetric non-linear sigma-models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy in QCD. Connections to other low-energy effective theories, in particular the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.

hep-th↗
arXiv2000

Measurement of Wave Chaotic Eigenfunctions in the Time-Reversal Symmetry-Breaking Crossover Regime

We present experimental results on eigenfunctions of a wave chaotic system in the continuous crossover regime between time-reversal symmetric and time-reversal symmetry-broken states. The statistical properties of the eigenfunctions of a two-dimensional microwave resonator are analyzed as a function of an experimentally determined time-reversal symmetry breaking parameter. We test four theories of one-point eigenfunction statistics and introduce a new theory relating the one-point and two-point statistical properties in the crossover regime. We also find a universal correlation between the one-point and two-point statistical parameters for the crossover eigenfunctions.

chao-dyn↗
arXiv1993

Dynamics of Earthquake Faults

We present an overview of our ongoing studies of the rich dynamical behavior of the uniform, deterministic Burridge--Knopoff model of an earthquake fault. We discuss the behavior of the model in the context of current questions in seismology. Some of the topics considered include: (1) basic properties of the model, such as the magnitude vs. frequency distribution and the distinction between small and large events; (2) dynamics of individual events, including dynamical selection of rupture propagation speeds; (3) generalizations of the model to more realistic, higher dimensional models; (4) studies of predictability, in which artificial catalogs generated by the model are used to test and determine the limitations of pattern recognition algorithms used in seismology.

adap-org↗
arXiv1998

Invariants and Labels in Lie-Poisson Systems

Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system.

chao-dyn↗
arXiv1999

Resource Letter TF-1: Turbulence in Fluids

This Resource Letter provides a guide to the literature on fully developed turbulence in fluids. It is restricted to mechanically driven turbulence in an incompressible fluid described by the Navier-Stokes equations of hydrodynamics, and places greatest emphasis on fundamental physical questions. Journal articles and books are cited for the following topics: The Navier-Stokes equations, qualitative aspects of turbulence, the 1941 Kolmogorov theory, intermittency and small scale structure, time correlations and pressure; with brief mention of two-dimensional turbulence, passive scalars in turbulence, and the turbulent boundary layer,

chao-dyn↗
arXiv1997

Chaos in the segments from Korean traditional singing and western singing

We investigate the time series of the segments from a Korean traditional song ``Gwansanyungma'' and a western song ``La Mamma Morta'' using chaotic analysis techniques. It is found that the phase portrait in the reconstructed state space of the time series of the segment from the Korean traditional song has a more complex structure in comparison with the segment from the western songs. The segment from the Korean traditional song has the correlation dimension 4.4 and two positive Lyapunov exponents which show that the dynamic related to the Korean traditional song is a high dimensional hyperchaotic process. On the other hand, the segment from the western song with only one positive Lyapunov exponent and the correlation dimension 2.5 exhibits low dimensional chaotic behavior.

chao-dyn↗
arXiv1998

Instability and Chaos in Non-Linear Wave Interaction: a simple model

We analyze stability of a system which contains an harmonic oscillator non-linearly coupled to its second harmonic, in the presence of a driving force. It is found that there always exists a critical amplitude of the driving force above which a loss of stability appears. The dependence of the critical input power on the physical parameters is analyzed. For a driving force with higher amplitude chaotic behavior is observed. Generalization to interactions which include higher modes is discussed. Keywords: Non-Linear Waves, Stability, Chaos.

chao-dyn↗
arXiv1999

Tri-axial Octupole Deformations and Shell Structure

Manifestations of pronounced shell effects are discovered when adding nonaxial octupole deformations to a harmonic oscillator model. The degeneracies of the quantum spectra are in a good agreement with the corresponding main periodic orbits and winding number ratios which are found by classical analysis.

nucl-th↗
arXiv1999

Chaos and order in a finite universe

All inhabitants of this universe, from galaxies to people, are finite. Yet the universe itself is often assumed to be infinite. If instead the universe is topologically finite, then light and matter can take chaotic paths around the compact geometry. Chaos may lead to ordered features in the distribution of matter throughout space.

astro-ph↗
arXiv1999

Noise-driven Synchronization in Coupled Map Lattices

Synchronization is shown to occur in spatially extended systems under the effect of additive spatio-temporal noise. In analogy to low dimensional systems, synchronized states are observable only if the maximum Lyapunov exponent $Λ$ is negative. However, a sufficiently high noise level can lead, in map with finite domain of definition, to nonlinear propagation of information, even in non chaotic systems. In this latter case the transition to synchronization is ruled by a new ingredient : the propagation velocity of information $V_F$. As a general statement, we can affirm that if $V_F$ is finite the time needed to achieve a synchronized trajectory grows exponentially with the system size $L$, while it increases logarithmically with $L$ when, for sufficiently large noise amplitude, $V_F = 0$ .

chao-dyn↗
arXiv1998

Melnikov's approximation dominance. Some examples

We continue a previous paper to show that Mel'nikov's first order formula for part of the separatrix splitting of a pendulum under fast quasi periodic forcing holds, in special examples, as an asymptotic formula in the forcing rapidity.

chao-dyn↗
arXiv1993

Life-Times of Simulated Traffic Jams

We study a model for freeway traffic which includes strong noise taking into account the fluctuations of individual driving behavior. The model shows emergent traffic jams with a self-similar appearance near the throughput maximum of the traffic. The lifetime distribution of these jams shows a short scaling regime, which gets considerably longer if one reduces the fluctuations for driving at maximum speed but leaves the fluctuations for slowing down or accelerating unchanged. The outflow from a traffic jam self-organizes into this state of maximum throughput.

cond-mat↗
arXiv1998

Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation

Successive pairs of pseudo-random numbers generated by standard linear congruential transformations display ordered patterns of parallel lines. We study the ``ordered'' and ``chaotic'' distribution of such pairs by solving the eigenvalue problem for two-dimensional modular transformations over integers. We conjecture that the optimal uniformity for pair distribution is obtained when the slope of linear modular eigenspaces takes the value $n_{opt} = maxint(p /\sqrt{p-1})$, where $p$ is a prime number. We then propose a new generator of pairs of independent pseudo-random numbers, which realizes an optimal uniform distribution (in the ``statistical'' sense) of points on the unit square $(0,1] \times (0,1]$. The method can be easily generalized to the generation of $k$-tuples of random numbers (with $k>2$)

chao-dyn↗
arXiv1999

An integration scheme for reaction-diffusion models

A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction-diffusion models. As paradigmatic examples of this class of partial differential equations the complex Ginzburg-Landau and the Fitzhugh-Nagumo equations have been analyzed. The novel algorithm has precision and stability comparable to those of pseudo-spectral codes, but it is more convenient to employ for systems with quite large linear extention $L$. As for finite-difference methods, the implementation of the present scheme requires only information about the local enviroment and this allows to treat also system with very complicated boundary conditions.

cond-mat.stat-mech↗
arXiv1994

On the local Hamiltonian structure of vector fields

We derive a canonical form for smooth vector fields on $\Re^{n+1}$. We use this to demonstrate the local multi-Hamiltonian nature of the corresponding flows. Associated with the canonical form is an inhomogenious linear PDE whose solutions provide conserved measures. These can be used to construct the local Hamiltonians.

chao-dyn↗