We show that the canonical invariant part of $ħ$ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable systems. We argue that the information content of the classical action and stability can be used more effectively than in the usual treatment. We demonstrate the improvement of precision on the example of the three disk scattering system.

We give evidence of coexisting transverse patterns of different symmetry in an optical beam circulating in a loop which contains a nonlinear medium. The symmetry of the patterns is controlled by the azimuthal rotation introduced in the feedback loop (nonlocality), while the competition is ruled by the input intensity which determines the distance from threshold (nonlinearity). Domains corresponding to patterns with different wave vectors (either different wavelength or different orientation) coexist, nucleating and moving. This gives rise to a complex spatiotemporal dynamics which is characterized by means of suitable collective indicators.

A Comment on the Letter by R. Jha et al., Phys. Rev. Lett. 69, 1375 (1992). The authors of the Letter offer a Reply.

A Reply to the Comment by Gautam C. Sethia and D. Chenna Reddy.

Recent work has considered the possibility of exploiting the phenomenon of chaos synchronization to achieve secure communication. But theoretical and experimental models studied thus far have been limited to low dimensional systems with one positive Lyapunov exponent. We investigate chaos synchronism in high dimensional systems. In particular, in regard to applications to communication, we show that by transmitting just one scalar signal one can achieve synchronism in chaotic systems with two or more positive Lyapunov exponents.

A light scattering experiment of turbulent convection in water is carried out in a convection cell with rough upper and lower surfaces. The vertical heat flux is found to be increased by $\sim 20\%$ when the Rayleigh number becomes larger than a transition value. The experiment reveals that the main effect of the surface roughness is to increase the emission of large thermal plumes, which travel vertically through the central region. These extra thermal plumes enhance the heat transport, and they are also responsible for the anisotropic behavior of velocity fluctuations at the cell center.

We experimentally observed patterns consisting of domains of upflow hexagons coexisting with domains of downflow hexagons in Boussinesq Rayleigh-Bénard convection. The sequence of patterns, as the control parameter $\epsilon =\Delta T/\Delta T_c-1\mathrm{}$ is increased, is from ordered or disordered rolls at onset to extended targets and spirals at $\epsilon \sim 1$, to coexisting hexagons at $\epsilon \sim 3$. Hexagons occur for all values of the Prandtl number $2.8\le P\le 28$ investigated. Surprisingly, they appear in a range where only rolls were known to be stable, and their wave number differs substantially from the roll wave number they coexist with.

A network of $N$ elements is studied in terms of a deterministic globally coupled map which can be chaotic. There exists a range of values for the parameters of the map where the number of different macroscopic configurations $N\left(N\right)$ is very large, $N\left(N\right)\sim \exp \sqrt{c\left(a\right)N}$, and there is violation of self-averaging. The time averages of functions, which depend on a single element, computed over a time $T$, have probability distributions that for any $N$ do not collapse to a delta function, for increasing $T$. This happens for both chaotic and regular motion, i.e., positive or negative Lyapunov exponent.

Properties of velocity circulation in three-dimensional turbulence are studied using data from high-resolution direct numerical simulation of Navier-Stokes equations. The probability density function (PDF) of the circulation depends on the area of the closed contour for which circulation is calculated, but not on the shape of the contour. For contours lying within the inertial range, the PDF has a Gaussian core with conspicuous exponential tails, indicating that intermittency plays an important role in circulation statistics. The measured scaling exponents are anomalous and substantially smaller than those implied by Kolmogorov's phenomenology.

A Comment on the Letter by Ditza Auerbach, Phys. Rev. Lett. 72, 1184 (1994). The authors of the Letter offer a Reply.

A Reply to the Comment by Carl Barratt.

We study the local scaling properties associated with straight line periodic orbits in homogeneous Hamiltonian systems, whose stability undergoes repeated oscillations as a function of one parameter. We give strong evidence of local scaling of the Poincaré section with exponents depending simply on the degree of homogeneity of the potential.

If one changes the control parameter of a chaotic system proportionally to the distance between an arbitrary point on the strange attractor and the actual trajectory, the lifetime τ of the most stable unstable periodic orbit in the vicinity of this point starts to diverge with a power law. The volume in parameter space where τ becomes infinite is finite and from its nonfractal boundaries one can determine directly the local Liapunov exponents. The experimental applicability of the method is demonstrated for two coupled diode resonators.

We show that a current-biased series array of nonidentical Josephson junctions undergoes two transitions as a function of the spread of natural frequencies. One transition corresponds to the onset of partial synchronization, and the other corresponds to complete phase locking. In the limit of weak coupling and disorder, the system can be mapped onto an exactly solvable model introduced by Kuramoto and the transition points can be accurately predicted.

The wave equation in a one–dimensional cavity is equivalent to the motion of massless particles in a two-dimensional space-time billiard. This allows us to consider, in a simple way, the case of a cavity with one or two oscillating walls. It is shown that a set of continuous families of frequencies of the oscillating walls leads to an exponential growth of the energy of a wave. For such cases, the wave energy is localized in narrow space regions moving at the wave velocity. As a consequence the electromagnetic vacuum fluctuations inside the cavity increase exponentially and the possibility to observe experimentally photon creation from the vacuum could be reconsidered.

The fundamental limits of the operation of quantum cascade intersubband lasers are investigated. Band nonparabolicities combined with the nonthermal electron distribution in the active region make laser action possible even in the absence of global $k$-space population inversion between subbands, i.e., when the lifetime of the lower subband exceeds that of the upper one. A laser based on local $k$-space population inversion with single-quantum-well active regions is demonstrated and its performance compared to that of quantum cascade lasers with double-quantum-well active regions.

We report the first demonstration of soft x-ray amplification in an elongated plasma column produced by laser irradiation of a gas puff target. The gas puff target is formed by the pulsed injection of gas from a high-pressure solenoid valve through a nozzle in the form of a narrow slit. The plasma column to be used as an x-ray laser active medium is produced by irradiating the gas puff target with a high-power laser beam focused to a line. Lasing in neonlike argon at 46.9 nm and strong indications of lasing in nickel-like xenon at 10.0 nm were observed.

We present analytical scaling results, confirmed by accurate numerics, to show that there exists a class of smoothly evolving zero surface tension solutions to the Hele-Shaw problem that are significantly perturbed by an arbitrarily small amount of surface tension in order one time.

We study a dynamically generated pattern in height gradients, centered around the active growth site, in the steady state of a self-organized interface depinning model. The pattern has a power-law tail and depends on the interface slope. An approximate integral equation relates the profile to local interface readjustments and long-ranged jumps of the active site. The pattern results in a two-point correlation function saturating to a finite value which depends on system size. Pattern formation is generic to systems in which the dynamics leads to correlated motion of the active site.

A high degree of control over the structure and dynamics of domain patterns in nonequilibrium systems can be achieved by applying nonuniform external fields near parity breaking front bifurcations. An external field with a linear spatial profile stabilizes a propagating front at a fixed position or induces oscillations with a frequency that scales like the square root of the field gradient. Nonmonotonic profiles produce a variety of patterns with controllable wavelengths, domain sizes, and frequencies and phases of oscillations.