We analyze quantum dynamical entropy based on the notion of coherent states. The mean value of this quantity for quantum maps on the sphere is computed as an average over the uniform measure on the space of unitary matrices of size $N$. Mean dynamical entropy is positive for $N\ge 3$, which supplies a direct link between random matrices of the circular unitary ensemble and the chaotic dynamics of the corresponding classical maps. Mean entropy tends logarithmically to infinity in the semiclassical limit $N\to \infty$ and this indicates the ubiquity of chaos in classical mechanics.

A model of two-dimensional arrays of Chua's circuits is numerically investigated. In a certain parameter region the spatiotemporal system has both synchronized oscillation and spiral wave attractors. Feedback pinnings are suggested to migrate the system from the spiral wave state to the coherent oscillation. The influences of the pinning density, forcing strength, and different pinning distributions on the driving effect are investigated. It is shown that some properly designed control schemes may reach very high control efficiency, i.e., killing a spiral wave consisting of a huge number of cells by injecting only very few cells. The wide applications of the approach are addressed.

By starting with the Maxwell theory of electromagnetism, we study the change of polarization state of light transmitting through optically anisotropic media. The basic idea is to reduce the Maxwell equation to the Schrödinger-like equation for two levels (or states) representing polarization. By using the quantum mechanical technique, the density matrix, and path integral, the evolution of the Stokes parameters results in the equation of motion for a pseudospin representing a point on the Poincaré sphere. Two typical examples relevant to actual experiments are considered; the one gives the generalized Faraday effect, and the other realizes an optical analog of magnetic resonance.

We have demonstrated two-dimensional double-diffusive convection in freely suspended soap films. The buoyancy due to heating and the film's tendency to stratify under gravity are competing mechanisms. The system is stable for a small temperature gradient and becomes unstable when the temperature gradient exceeds a certain threshold. It is experimentally shown that the primary instability is an oscillatory state consisting of a standing-wave pattern. This is in agreement with our linear stability analysis.

For the one-dimensional complex Ginzburg-Landau equation (CGLE) we obtain, by a shooting algorithm, a family of uniformly propagating hole solutions which differ from the well-known Nozaki-Bekki holes. These holes occur in many regimes of the CGLE, most prominently in the regime known as spatiotemporal intermittency. A stability analysis reveals that these holes have one unstable core mode, and we discuss the consequence of this for the intermittent states.

When two identical chaotic oscillators interact, one or more intervals of coupling parameters generally exist in which the synchronized state is weakly stable and its basin of attraction is riddled with holes that are repelled from it. Here, we discuss the role of the absorbing area for the emergence of local vs global riddling and for controlling the dynamics, once the synchronization breaks down.

Phase synchronization of chaos is studied using a modified Rössler system. By employing a lift of the phase variable (i.e., phase points separated by $2\pi$ are not considered as the same), the transition to phase synchronization is viewed as a boundary crisis mediated by an unstable-unstable pair bifurcation on a branched manifold, and the accompanying basin boundary structure is found to be of a new type.

An energy eigenfunction in a classically chaotic system is known to have spatial correlations which (in the limit of small $ħ$) are governed by a microcanonical distribution in the classical phase space. This result is valid, however, only over coordinate distances which are small compared to any relevant classical distance scales (such as the cyclotron radius for a charged particle in a magnetic field). We derive a modified formula for the correlation function in the regime of large separation. This then permits a complete description, over all length scales, of the statistical properties of chaotic eigenfunctions in the $ħ\to 0$ limit. Applications to quantum dots are briefly discussed.

We analyze the relaxation of fronts propagating into unstable states. While “pushed” fronts relax exponentially like fronts propagating into a metastable state, “pulled” or “linear marginal stability” fronts relax algebraically. As a result, for thin fronts of this type, the standard moving boundary approximation fails. The leading relaxation terms for velocity and shape are of order $1/t$ and $1/t^{3/2}$. These universal terms are calculated exactly with a new systematic analysis that unifies various heuristic approaches to front propagation.

Shock-tube experiments were performed in order to verify recently developed theoretical models for the evolution of the shock-wave induced Richtmyer-Meshkov instability [Phys. Rev. Lett. 74, 534 (1995)]. Single-mode bubble and spike evolution and two-bubble interaction in both early and late nonlinear stages were investigated in a $M\approx 1.3$ $\mathrm{Air}-\mathrm{to}-{\mathrm{SF}}_6$ shock-tube experiment. Experimental results for the single-mode and two-bubble cases, showing distinct bubble and spike evolution, were found to be in very good agreement with the theoretical model prediction as well as numerical simulations, verifying the key elements of the bubble-merger model used for the prediction of the multimode bubble and spike front evolution.

A Comment on the Letter by Brian R. Hunt and Edward Ott, Phys. Rev. Lett. 76, 2254 (1996). The authors of the Letter offer a Reply.

A Reply to the Comment by Scott M. Zoldi and Henry S. Greenside.

Embedding techniques for predicting chaotic time series from experimental data may fail if the reconstructed attractor self-intersects, and such intersections often occur unless the embedding dimension exceeds twice the attractor's box counting dimension. Here we consider embeddings with self-intersection. When the dimension $M$ of the measurement space exceeds the information dimension $D_1$ of the attractor, reliable prediction is found to be still possible from most orbit points. In particular, the fraction of state space measure from which prediction fails typically scales as ${\varepsilon }^{{M-D}_1}$ for small $\varepsilon$ where $\varepsilon$ is the diameter of the current state's neighborhood used for prediction.

As examples of quantum-“classical” coupling systems, multicomponent systems are studied by semiclassical evaluations of the Feynman kernels in the coherent-state representation. From the observation of the phase space caustics, due to the presence of the internal degree of freedom (IDF), two phenomena are explained in terms of the semiclassical theory: (1) The quantum oscillations of the IDF induce quantum interference patterns in the Hushimi representation and (2) chaotic dynamics destroys the coherence of the quantum oscillations.

We introduce a method for reconstructing quantum superposition states excited in molecules or atoms by short laser pulses. The technique is based on mixing the unknown object state with a known reference state generated in the same system by an additional delayed laser pulse, and detecting the total time- and frequency-integrated fluorescence as a function of the delay. We demonstrate the feasibility of the method by reconstructing various vibrational wave packets in sodium dimers.

We give a classical geometric optics description of incoherent solitons—those launched by a diffuse source. This method is intuitive, advances predictions such as the existence of solitons of arbitrary cross section, and importantly, it provides a simple (universal) analytical description for the incoherent solitons of any nonlinear medium. Previously, analytical results were known for the $\ln I$ nonlinearity only.

We consider the coupled higher order nonlinear Schrödinger (CHNLS) equations which govern the propagation of the fields in a birefringent fiber with all higher order effects like the third order dispersion, Kerr dispersion, and stimulated Raman scattering. We generalize the $2\times 2$ Ablowitz-Kaup-Newell-Segur method to the $5\times 5$ eigenvalue problem and construct the Lax pair. The exact soliton solutions are explicitly obtained using the Darboux-Bäcklund transformation. A similar case of study is extended to three coupled HNLS equations and hence generalized to $N$-coupled equations.

We present evidence, based on lattice Boltzmann simulations, to show that the coarsening of the domains in phase-separating binary fluids is not a scale-invariant process. Moreover we emphasize that the pathway by which phase separation occurs depends strongly on the relation between diffusive and hydrodynamic time scales.

We explore the Saffman-Taylor instability of a gas bubble expanding into a shear thinning liquid in a radial Hele-Shaw cell. Using Darcy's law generalized for non-Newtonian fluids, we perform simulations of the full dynamical problem. The simulations show that shear thinning significantly influences the developing interfacial patterns. Shear thinning can suppress tip splitting, and produce fingers which oscillate during growth and shed side branches. Emergent length scales show reasonable agreement with a general linear stability analysis.