Unnested islands of period-doublings in an injected semiconductor laser

We present a theoretical study of unnested period-doubling islands in three-dimensional rate equations modeling a semiconductor laser subject to external optical injection. In this phenomenon successive curves of period doublings are not arranged in nicely nested islands, but intersect each other. This overall structure is globally organized by several codimension-2 bifurcations. As a consequence, the chaotic region existing inside an unnested island of period doublings can be entered not only via a period-doubling cascade but also via the breakup of a torus, and even via the sudden appearance of a chaotic attractor. In order to fully understand these different chaotic transitions we reveal underlying global bifurcations and we show how they are connected to codimension-2 bifurcation points. Unnested islands of period doublings appear to be generic and hence must be expected in a large class of dynamical systems

Pure scaling operators at the integer quantum Hall plateau transition

Stationary wave functions at the transition between plateaus of the integer quantum Hall effect are known to exhibit multi-fractal statistics. Here we explore this critical behavior for the case of scattering states of the Chalker-Coddington model with point contacts. We argue that moments formed from the wave amplitudes of critical scattering states decay as pure powers of the distance between the points of contact and observation. These moments in the continuum limit are proposed to be correlations functions of primary fields of an underlying conformal field theory. We check this proposal numerically by finite-size scaling. We also verify the CFT prediction for a 3-point function involving two primary fields.Comment: Published version, 4 pages, 3 figure

Statistics of conductance and shot-noise power for chaotic cavities

We report on an analytical study of the statistics of conductance, $g$, and shot-noise power, $p$, for a chaotic cavity with arbitrary numbers $N_{1,2}$ of channels in two leads and symmetry parameter $\beta = 1,2,4$. With the theory of Selberg's integral the first four cumulants of $g$ and first two cumulants of $p$ are calculated explicitly. We give analytical expressions for the conductance and shot-noise distributions and determine their exact asymptotics near the edges up to linear order in distances from the edges. For $0<g<1$ a power law for the conductance distribution is exact. All results are also consistent with numerical simulations.Comment: 7 pages, 3 figures. Proc. of the 3rd Workshop on Quantum Chaos and Localisation Phenomena, Warsaw, Poland, May 25-27, 200

Multipulse excitability in injected lasers

We show that a single-mode semiconductor laser subject to optical injection, and described by rate equations, can produce excitable multipulses, where the laser emits a certain number of pulses after being triggered from its steady state by a single perturbation. This phenomenon occurs in experimentally accessible regions in parameter space that are bounded by curves of n-homoclinic bifurcations, connecting a saddle to itself only at the n-threturn to a neighborhood of the saddle. These regions are organised in what we call 'homoclinic teeth' that grow in size and shape with the linewidth enhancement factor

Multipulse excitability in a semiconductor laser with optical injection

A deterministic mechanism for multipulse excitability that appears to be experimentally accessible in a real laser is presented. Codimension-two homoclinic Belyakov bifurcations and an ensuing cascade of n-homoclinic bifurcation tongues are described as responsible for this phenomenon

Asian development pathways and sustainable socio-technical regimes

Rapid industrialisation in Asia is generating a significant new demand for raw materials and pressure on local, regional and global environments. In the future these demands and pressures are expected to increase markedly. These concerns are models of development that assume that economic growth follows a pattern leading to a convergence between the structure, growth and productivity of economies over the long run. In these models, the structure of industries and sectors, technological capabilities and consumer preferences are regarded as converging towards patterns established in more advanced economies. By extension, convergence is also assumed to hold for the resource intensity and environmental pressure associated with growth in industrialising countries. This paper argues for greater attention to the resource and environmental quality of development. It argues that by applying ideas from an emerging literature on 'systems innovation' it becomes possible to envisage the emergence of new, more resource-efficient socio-technical systems as the basis of more sustainable development pathways in developing Asia. Such sustainable socio-technical systems will emerge in the context of interaction between domestic and globalised markets, knowledge flows and governance. Key issues for a research agenda are set out. © 2008 Elsevier Inc. All rights reserved

Global quantitative predictions of complex laser dynamics

We demonstrate unprecedented agreement between a theoretical two-dimensional bifurcation diagram and the corresponding experimental stability map of an optically injected semiconductor laser over a large range of relevant injection parameter values. The bifurcation diagram encompasses both local and global bifurcations mapping out regions of regular, chaotic, and multistable behavior in considerable detail. This demonstrates the power of dynamical systems modeling for the quantitative prediction of nonlinear dynamics and chaos of semiconductor lasers