Semiclassical mechanics of bound chaotic potentials

Semiclassical methods for determining quantum eigenvalues in chaotic systems are discussed. A recent calculation for an open scattering system with Axiom-A properties serves as a starting point for the discussion. How deviation from Axiom-A properties, such as intermittency and occurrence of small stability islands, normally arise in bound Hamiltonian systems, and how these deviations complicate the calculation of semiclassical eigenvalues are demonstrated. It is also stressed that since such deviations are typical of bound Hamiltonian systems, they might be of crucial importance for the statistical properties of the energy levels.     

Resonances in chaotic dynamics

We present a discussion and some numerical results on the actual possibility of making accessible, by numerical techniques, the complex singularities of the power spectrum (resonances) for a chaotic signal. Hénon's transformation is investigated in detail, showing that the position of the leading resonance in the complex frequency plane determines the kind of mixing rate in the time evolution.     

Attractor selection in chaotic dynamics

For different settings of a control parameter, a chaotic system can go from a region with two separate stable attractors (generalized bistability) to a crisis where a chaotic attractor expands, colliding with an unstable orbit. In the bistable regime jumps between independent attractors are mediated by external perturbations; above the crisis, the dynamics includes visits to regions formerly belonging to the unstable orbits and this appears as random bursts of amplitude jumps. We introduce a control method which suppresses the jumps in both cases by filtering the specific frequency content of one of the two dynamical objects. The method is tested both in a model and in a real experiment with a CO2 laser.     

Stochastic resonance in chaotic dynamics

It is suggested that chaotic dynamical systems characterized by intermittent jumps between two preferred regions of phase space display an enhanced sensitivity to weak periodic forcings through a stochastic resonance-like mechanism. This possibility is illustrated by the study of the residence time distribution in two examples of bimodal chaos: the periodically forced Duffing oscillator and a 1-dimensional map showing intermittent behavior.     

Recent developments in chaotic dynamics

A brief review of chaotic dynamics is presented. Topics discussed include basic concepts, recent developments, and applications     

Quantum freeze of fidelity decay for chaotic dynamics

We show that the mechanism of quantum freeze of fidelity decay for perturbations with a zero time average, recently discovered for a specific case of integrable dynamics [New J. Phys. 5, 109 (2003)], can be generalized to arbitrary quantum dynamics. We work out explicitly the case of a chaotic classical counterpart, for which we find semiclassical expressions for the value and the range of the plateau of fidelity. After the plateau ends, we find explicit expressions for the asymptotic decay, which can be exponential or Gaussian depending on the ratio of the Heisenberg time to the decay time. Arbitrary initial states can be considered; e.g., we discuss coherent states and random states.     

Using synchronization for prediction of high-dimensional chaotic dynamics

We experimentally observe the nonlinear dynamics of an optoelectronic time-delayed feedback loop designed for chaotic communication using commercial fiber optic links, and we simulate the system using delay differential equations. We show that synchronization of a numerical model to experimental measurements provides a new way to assimilate data and forecast the future of this time-delayed high-dimensional system. For this system, which has a feedback time delay of 22 ns, we show that one can predict the time series for up to several delay periods, when the dynamics is about 15 dimensional.     

Extreme value distributions in chaotic dynamics

A theory of extremes is developed for chaotic dynamical systems and illustrated on representative models of fully developed chaos and intermitent chaos. The cumulative distribution and its associated density for the largest value occurring in a data set, for monotonically increasing (or decreasing) sequences, and for local maxima are evaluated both analytically and numerically. Substantial differences from the classical statistical theory of extremes are found, arising from the deterministic origin of the underlying dynamics.     

Yb离子抽运动力学及脉冲储能特性研究

从准三能级Yb离子的能级结构出发，建立了Yb离子的抽运和激光速率方程，结合解析和数值方法，研究了Yb激光介质的抽运动力学过程，包括抽运激发效率、最低抽运强度、激光能量提取效率等关键参数.比较了三类典型的Yb激光介质性能：Yb:S-FAP,Yb:YAG以及Yb:FP-glass.以放大自发辐射(ASE)为设计判据，重点研究了脉冲储能型Yb激光器的设计准则，包括增益介质的厚度与掺杂浓度.最后利用此模型给出了基于Yb:S-FAP以及Yb:YAG的100J级二极管抽运固体激光器(DPSSL)的总体设计参数.将对基于Yb激光介质的脉冲储能型DPSSL的设计提供有益的参考. 关键词： Yb离子 速率方程 抽运动力学 二极管抽运固体激光器     

Simulation of chaotic behaviour in population dynamics

In the time evolution of populations, many attractors can be found: fixed points, limit cycles and chaotic regimes. Usually, chaotic behaviour is observed in species which have well defined breeding seasons and a high fertility rate. Different mathematical models have been used in order to simulate those regimes. In this paper, we use the bitstring model introduced to simulate the evolution of age-structured populations -- the Penna Model -- to simulate a sort of cyclic and chaotic behaviours. In comparison with the standard logistic map, our results show a time changing parameter. Received: 5 August 1997 / Revised: 8 November 1997 / Accepted: 13 November 1997     

Fluctuations and simple chaotic dynamics

We describe the effects of fluctuations on the period-doubling bifurcation to chaos. We study the dynamics of maps of the interval in the absence of noise and numerically verify the scaling behavior of the Lyapunov characteristic exponent near the transition to chaos. As previously shown, fluctuations produce a gap in the period-doubling bifurcation sequence. We show that this implies a scaling behavior for the chaotic threshold and determine the associated critical exponent. By considering fluctuations as a disordering field on the deterministic dynamics, we obtain scaling relations between various critical exponents relating the effect of noise on the Lyapunov characteristic exponent. A rule is developed to explain the effects of additive noise at fixed parameter value from the deterministic dynamics at nearby parameter values.     

Lower bound on neutrino pair emission

Weak neutral currents affect the rates with which stars lose energy by emitting neutrino pairs. These rates can be calculated once the parameters of the underlying theory are fixed. Here we show that any new gauge theory will have a minimum rate, equal to half the old rate. The proof rests on the (assumed) μe universality of neutral currents. We also speculate on the possible existence of new types of neutrinos which may considerably enhance stellar cooling. The minimum becomes $\text{(}\text{(n+1)}\text{(n+2)}\text{)}$ times the old rate, where n=number of new neutrinos.     

The evolution of chaotic dynamics for fractional unified system

Based on reliable numerical approach, this Letter studies the chaotic behavior of the fractional unified system. The lowest orders for this system to have a complete chaotic attractor (the attractor covers the three equilibrium points of the classical unified system) at different parameter values are obtained. A striking finding is that with the increase of the parameter α of the fractional unified system from 0 to 1, the lowest order for this system to have a complete chaotic attractor monotonically decreases from 2.97 to 2.07. Because of the inherent attribute (memory effects) of fractional derivatives, this finding reveals that the chaotic behavior of fractional (classical) unified system becomes stronger and stronger when α increases from 0 to 1. Furthermore, this Letter introduces a novel measure to characterize the chaos intensity of fractional (classical) differential system.     

Molecular dynamics for collisions of heavy ions

Ying-Xun Zhang, Ning Wang, and their collaborators systematically reviewed the molecular dynamics and its application to heavy ion collisions at low and intermediate energies [6].     

The effect of atomic dynamics on the energy loss of ions channeled in carbon nanotubes

Channeling of atomic particles in carbon nanotubes was studied by molecular dynamics methods. It was shown that the elastic energy loss of sufficiently heavy incident particles due to carbon atoms becomes significant at low energies and angles close to the critical channeling ones.     

Anticipating the dynamics of chaotic maps

We study the regime of anticipated synchronization in unidirectionally coupled chaotic maps such that the slave map has its own output re-injected after a certain delay. For a class of simple maps, we give analytic conditions for the stability of the synchronized solution, and present results of numerical simulations of coupled 1D Bernoulli-like maps and 2D Baker maps, that agree well with the analytic predictions.     

Noise can reduce disorder in chaotic dynamics

We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or natural measure) is generally highly inhomogeneous over the set, either diminishing or enhancing the contribution of these orbits into system dynamics. We show analytically and numerically a weak noise to reduce this inhomogeneity and, additionally to obvious perturbing impact, make a regularizing influence on the chaotic dynamics. This universal effect is rooted into the nature of deterministic chaos.     

Metabolic network dynamics in open chaotic flow

We have analyzed the dynamics of metabolically coupled replicators in open chaotic flows. Replicators contribute to a common metabolism producing energy-rich monomers necessary for replication. The flow and the biological processes take place on a rectangular grid. There can be at most one molecule on each grid cell, and replication can occur only at localities where all the necessary replicators (metabolic enzymes) are present within a certain neighborhood distance. Due to this finite metabolic neighborhood size and imperfect mixing along the fractal filaments produced by the flow, replicators can coexist in this fluid system, even though coexistence is impossible in the mean-field approximation of the model. We have shown numerically that coexistence mainly depends on the metabolic neighborhood size, the kinetic parameters, and the number of replicators coupled through metabolism. Selfish parasite replicators cannot destroy the system of coexisting metabolic replicators, but they frequently remain persistent in the system. (c) 2002 American Institute of Physics.