Criteria for ergodicity and rates of energy flow in a quantum mechanical system of $N$ coupled anharmonic oscillators where $N$ is large are determined at energies near the ground state of the system. High-order resonances are important for the transition at large $N$. The role of numerous virtual transitions, “vibrational superexchange,” in global transport is examined both for typical parts of the state space and special states often interrogated experimentally.

We report the first experimental observation of irregular picosecond light pulses within the coherence collapse of a semiconductor laser subject to delayed moderate optical feedback. This pulsing behavior agrees with the recent explanation of low frequency fluctuations as chaotic itinerancy with a drift. Theory and experiments show very good agreement.

A new physical effect, turbulent thermal diffusion, is discussed. This phenomenon is related to the dynamics of small inertial particles in incompressible turbulent fluid flow. At large Reynolds and Peclet numbers the turbulent thermal diffusion is much stronger than the molecular thermal diffusion. It is shown that inertia of particles under certain conditions can cause a large-scale instability of spatial distribution of particles. Inertial particles are concentrated in the vicinity of the minimum (or maximum) of the mean temperature of the surrounding fluid depending on the ratio of material particle density to that of the surrounding fluid.

Ordered states of cellular flames consist of concentric rings of luminous cells. These states are observed to bifurcate to ratcheting states in which one or more rings drift $(\sim 1\mathrm{deg}/\sec )$ in a circular path, speeding up and slowing down in a characteristic manner. Experimental results from three ratcheting states are presented: one in which two rings of cells ratchet together; one in which an outer ring ratchets, locked with the inner ring through an angle, until the inner ring unlocks and snaps back to its original position; and one in which an outer ring ratchets and an inner ring remains fixed. These results are discussed in the context of bifurcations in symmetric systems.

The redistribution of conserved quantities among colliding solitons of the nonlinear Schrödinger equation is considered. An analogy with the theory of spatial solitons in nonlinear optics provides one way to calculate this redistribution. In this context, exchanges of conserved quantities among $N$ colliding solitons can be completely described from a knowledge of the case for $N=2\mathrm{}$. It is shown that solitons generally exchange $L^2$ norm as they collide, with the fraction shared being small when the solitons differ significantly in velocity or amplitude. Exchanges of other conserved densities are also considered.

Experiments in rupture of mercury drops have been performed recording the size distribution of the cumulative number of drops for different conditions of rupture. A transition of the distribution from log-normal to scaling behavior is shown. To describe it, a geometric probabilistic model is proposed. Consequently, the rupture can be described as a process of percolation in a Bethe lattice. Then, the rupture process and the transition to scaling can be viewed as a problem of phase transition. Comparison with several fracture experimental data is also made showing the possibilities of this viewpoint.

The evidence of square patterns in Bénard-Marangoni convection relatively far above threshold is demonstrated for the first time by means of a direct numerical integration of the three-dimensional Navier-Stokes equations. It is shown that regular squares are only obtained for a finite Prandtl number. Finally a qualitative explanation of the obtained sequence of instabilities based on a model of amplitude equations is discussed.

A Comment on the Letter by C. Van den Broeck, J. M. R. Parrondo, and R. Toral, Phys. Rev. Lett. 73, 3395 (1994). The authors of the Letter offer a Reply.

A Reply to the Comment by Sriram Ramaswamy, Rahul Pandit, and Rangan Lahiri.

In this Letter, we propose a simple chaotic signal masking scheme employing Chua's circuit without the requirement of chaos synchronization. Although, in general, our procedure involves the inverse system approach, the resulting inverse system in our case is a linear one. Therefore, the difficulty of inverse realization of the transmitter's nonlinear parts also at the receiving end, which is encountered in the general scheme of the inverse system approach, is eliminated.

We report the first direct experimental realization of the quantum $\delta$-kicked rotor. Our system consists of a dilute sample of ultracold sodium atoms in a periodic standing wave of near-resonant light that is pulsed on periodically in time to approximate a series of delta functions. Momentum spread of the atoms increases diffusively with every pulse until the "quantum break time" after which exponentially localized distributions are observed. Quantum resonances are found for specific values of the pulse period.

We present a universal mechanism which allows us to relinquish momentum population inversion in free-electron lasers, and extract strongly enhanced gain from a broad momentum distribution. This is achievable by appropriately designed magnetic fields between two sequential interaction regions, which cause, purely classically, absorption cancellation (by destructive interference) and emission enhancement (by constructive interference).

We demonstrate experimentally that the intensity noise of so-called "free-running single-mode" laser diodes results from a cancellation between very large anticorrelated fluctuations of the main mode, on one hand, and of many weak longitudinal side modes, on the other hand. When line narrowing techniques are used, intensity squeezing can be observed at room temperature, but this noise reduction is not always single-mode squeezing. These experimental results are in agreement with a simple phenomenological model using Langevin-type equations.

We report on some surprising structures of particle paths in the velocity field of wavy Taylor vortices using velocity fields from a model of Davey, DiPrima, and Stuart [J. Fluid Mech. 31, 17-52 (1968)]. We observe that there are regions of chaotic mixing in the boundaries between the vortices and, more surprisingly, find evidence of ring vortices propagating azimuthally around the cylinder at the speed of the wave propagation.

We formulate the theory of surface tension driven Stokes flow set up by an active scalar with zero diffusivity. The 3D hydrodynamic problem can be reduced to a 2D nonlinear evolution equation involving only free surface quantities. For a semi-infinite layer it can be rigorously demonstrated that the solutions to this equation blow up in finite time and develop singular forms. The new type of nonlinearity plays a universal role in the description of interfacial turbulence.

The origin of the low frequency oscillation of the large-scale, recirculating flow specific to the high Rayleigh number regime in closed convection cells is investigated. It is shown how the oscillations result from the delayed coupling of the boundary layer instabilities by the slow convective motion of the recirculation. The model developed explains (i) the form of the dependence of the oscillation frequency with the Rayleigh number $f\sim {\mathrm{Ra}}^{\gamma }$, including the prefactor, the "anomalous" value of the exponent $\gamma \approx 0.49$, and (ii) the opposition of phase of the oscillations between the top and bottom boundary layers.

The relation between disordered and chaotic systems is investigated. It is obtained by identifying the diffusion operator of the disordered systems with the Perron-Frobenius operator in the general case. This association enables us to extend results obtained in the diffusive regime to general chaotic systems. In particular, the two-point level density correlator and the structure factor for general chaotic systems are calculated and characterized. The behavior of the structure factor around the Heisenberg time is quantitatively described in terms of short periodic orbits.

The motion of a classical particle in a convex plane region with softened boundary is considered. The Kolmogorov-Arnol'd-Moser theory is applied to detect "whispering gallery" trajectories, i.e., solutions staying near the boundary. It turns out that the large energy solutions starting near the boundary are quasiperiodic and stay there for all time filling out the invariant tori in the phase space, under some regularity conditions on the force repelling the particle from the boundary. The same technique is applied to the analysis of propagation of a skew light ray through the optical fiber with nonuniform core. It is shown that the majority of skew light rays starting near the boundary of the fiber stay there for all time under some restrictions on the refraction index.

Laboratory studies reveal a deformational instability that leads to a drained region (dry spot) in an initially flat liquid layer (with a free upper surface) heated uniformly from below. This long-wavelength instability supplants hexagonal convection cells as the primary instability in viscous liquid layers that are sufficiently thin or are in microgravity. The instability occurs at a temperature gradient 35% smaller than predicted by linear stability theory. Numerical simulations show a drained region qualitatively similar to that seen in the experiment.

We demonstrate that the quantum localization (narrowed momentum distributions) observed in the recent momentum transfer experiments may be associated with the influence of classical phase space resonance structures on quantum Floquet states. By numerically investigating the evolution of initial distributions located in chaotic regions of the classical phase space, we argue that dynamical localization, seen, for example, in quantum kicked rotor models, is not the only possible explanation of the observed localized momentum distributions.