We study fluctuations of survival probability in an open quantum system classically described by a map with a mixed phase space. Our results provide the first numerical support to theoretical predictions that such fluctuations have a fractal structure, quantitatively related to the algebraic decay of the classical survival probability.

For a finite-dimensional dynamical system, whose governing equations may or may not be analytically available, we show how to stabilize an unstable orbit in a neighborhood of a “fully”unstable fixed point (i.e., a fixed point at which all eigenvalues of the Jacobian matrix have modulus greater than unity). Only one of the unstable directions is to be stabilized via time-dependent adjustments of control parameters. The parameter adjustments can be optimized.

It is shown experimentally that the nonspecular reflection of light on an interface induces a time delay, as predicted by Wigner's scattering theory. A differential femtosecond technique is used to directly isolate this delay, associated with the Goos-Hänchen spatial shift produced by a grating near a resonant Wood anomaly. A delay of 4.4 fs is observed between TE and TM pulses, in agreement with the expected Wigner delay obtained from phase shift dispersion measurements.

We show the existence of discrete sets of Raman sidebands which self-consistently establish a Raman coherence and propagate without change in amplitude and relative phase. Equivalently, there exist periodic femtosecond-time-scale, temporal pulse shapes which propagate without change in shape.

The second-order nonlinear optical coefficients associated with chirality differ in sign for the two mirror-image forms (enantiomers) of a chiral material. Structures comprised of alternating stacks of the enantiomers can therefore be used for quasi-phase-matched frequency conversion, as we demonstrate here by second-harmonic generation from Langmuir-Blodgett films of a helicenebisquinone. Such structures could lead to new types of frequency converters in which both the second-order nonlinear response and quasi-phase-matching arise from the chirality of a material rather than its polar order.

Photorefractive spatial screening solitons are treated as rays using geometrical optics. The ray picture is transformed into a classical mechanics picture, in which solitons move self-consistently as particles in a potential created by the induced change in the refractive index. The Hamiltonian equations of motion are integrated to yield trajectories that agree with the optical center-of-mass trajectories. The motion in the transverse plane is found to be not central and the orbits are not closed, preventing the spiraling of solitons.

We report on the first quantitative observations of convection in a fluid layer driven by both heating from below and vertical sinusoidal oscillation. Just above onset, convection patterns are modulated either harmonically or subharmonically to the drive frequency. Single-frequency patterns exhibit nearly solid-body rotations with harmonic and subharmonic states always rotating in opposite directions. Flows with both harmonic and subharmonic responses are found near a codimension-two point, yielding novel coexisting patterns with symmetries not found in either single-frequency states. Predictions from linear stability analysis of the onset Rayleigh and wave numbers compare well with experiment, and phase boundaries for coexisting patterns track single-frequency marginal stability curves.

We analyze phase separation in ternary systems in the asymptotic hydrodynamic regime when the volume fractions and concentrations are constant. The multiphase Navier-Stokes equations are solved using a level set method. A new projection method was developed to treat multiple junctions for systems with more than two phases. It is found that surface tension ratios can alter the growth mechanism of a minority phase in the presence of two majority phases. When the minority phase wets the interface of the majority phases the domain growth rate of all three phases is initially similar to that of a symmetric binary fluid but slows down at later times.

We use the coherent density function theory to show that partially coherent beams are unstable and may collapse in inertial bulk Kerr media. The threshold power for collapse, and its dependence on the degree of coherence, is found analytically and checked numerically. The internal dynamics of the walk-off modes is illustrated for collapsing and diffracting partially coherent beams.

We demonstrate that frequency-domain interferometry can be performed in the extreme ultraviolet range using high-order harmonics. We first show that two phase-locked harmonic sources delayed in time can be generated in the same medium despite ionization. This gives insight into the dynamics of the generation and ionization processes. We then apply the technique to the study of the temporal evolution of an ultrashort laser-produced plasma at the femtosecond time scale.

Using orthonormal divergence-free vector wavelets, we analyzed the nonlinear transfer in three-dimensional homogeneous, isotropic turbulence. Wavelet analysis supports the predominance of local interactions in the nonlinear energy transfer process, which is consistent with Kolmogorov's phenomenology. Analogous Fourier analysis is also carried out for comparison. It is verified that the predominance of nonlocal interactions [J. A. Domaradzki and R. S. Rogallo, Phys. Fluids A 2, 413 (1990); P. K. Yeung and J. G. Brasseur, Phys. Fluids A 3, 884 (1991); K. Ohkitani and S. Kida, Phys. Fluids A 4, 794 (1992)] results from linearly binned Fourier analysis, whose shortcomings are also discussed.

A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be recovered from the time-averaged predictions of the reduced model. A Liouville theorem leads to inviscid equipartition solutions. Excellent agreement is obtained with two-dimensional forced-dissipative pseudospectral simulations. For the two-dimensional enstrophy cascade, logarithmic corrections to the high-order structure functions are observed.

The transition to fully developed turbulence of a wake flow is investigated on different length scales $r$. It is shown that the $r$ dependence of the velocity increments can be taken as Markov processes even in the case of not fully developed turbulence. The estimation of the deterministic part of these Markov processes shows a pronounced structural change as one passes away from the cylinder, which can be parametrized by a kind of order parameter. We propose that this effect is connected to the presence of large scale coherent structures close to the cylinder.

The large scale properties of spatiotemporal chaos in the 2D Kuramoto-Sivashinsky equation are studied using an explicit coarse-graining scheme. A set of intermediate equations are obtained which describe interactions between the small scale structures and the hydrodynamic degrees of freedom. Possible forms of the effective large scale hydrodynamics are constructed and examined. Although a number of different universality classes are allowed by symmetry, numerical results support the simplest scenario, that being the Kardar-Parisi-Zhang universality class.

Light propagating in an optically thick sample experiences multiple scattering. It is now known that interferences alter this propagation, leading to an enhanced backscattering, a manifestation of weak localization of light in such diffuse samples. This phenomenon has been extensively studied with classical scatterers. In this Letter we report the first experimental evidence for coherent backscattering of light in a laser-cooled gas of rubidium atoms.

High harmonic radiation spectra up to 19th order in alkali metal vapors excited by an intense, picosecond mid-infrared ( $3–4\mu \mathrm{m}$) laser are reported and compared to theory. The strong-field dynamics in the alkali metal atoms exhibit significant differences from all previously studied systems due to the strong coupling between their ground and first excited states.

It is shown that for a simple face-centered-cubic lattice of spherical scatterers more than one complete photonic band gap (CPBG) can open and the relative gap width can be as large as $10\%$ even if the host dielectric constant ${\varepsilon }_h=1\mathrm{}$. The key is to use the spheres made out of material having a Drude-like behavior of the dielectric function, and, to tune lattice spacing appropriately to a characteristic plasma wavelength. We argue that such structures can provide CPBG structures with tunable band gaps down to ultraviolet wavelengths.

We have observed transverse pattern formation in a near-confocal, type II, triply resonant optical parametric oscillator (OPO) operating close to frequency degeneracy for the signal and idler modes. In the region of observation of these patterns, the OPO oscillation threshold increases. Complex ring patterns and latticelike structures are observed. These patterns are due to the nonlinear coupling of many transverse modes (on the order of 25). The transverse distribution of the light is different in the signal, idler, and transmitted pump modes.

We present experimental results for wave numbers $q_s$ selected in a thin horizontal fluid layer heated from below. The cylindrical sample had an interior section of uniform spacing ${d=d}_0$ for radii $r<\mathrm{}{r}_0$ ( ${\Gamma }_0\equiv r_0/d_0=43\mathrm{}$) and a ramp $d\left(r\right)$ for $r>\mathrm{}{r}_0$. For Rayleigh numbers $R_0>R_c=1708\mathrm{}$ in the interior, straight or slightly curved rolls with an average $〈q_s〉={\tilde{q}}_c+\alpha {\epsilon }_0({\epsilon }_0\equiv R_0/R_c-1\mathrm{})$ and ${\tilde{q}}_c<q_c=3.117\mathrm{}$ were selected, and $q_s$ varied on two length scales approximately equal to ${\Gamma }_0$ and to four roll wavelengths. For $\epsilon \lesssim 0.03$ and $\epsilon \gtrsim 0.18$ the pattern repeatedly formed defects.

A Comment on the Letter by E. P. Petrov, et al. Phys. Rev. Lett. 81, 77 (1998). The authors of the Letter offer a Reply.