We numerically analyze quantum survival probability fluctuations in an open, classically chaotic system. In a quasiclassical regime and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal pattern, on the grounds of semiclassical arguments. In contrast, we work in a classical regime of complete chaoticity and in a deep quantum regime of strong localization. We provide evidence that fluctuations are still fractal, due to the slow, purely quantum algebraic decay in time produced by dynamical localization. Such findings considerably enlarge the scope of the existing theory.

Using a model of high-harmonic generation that couples a fully quantum calculation with a semiclassical electron trajectory picture, we show that a new type of phase matching is possible when an atom is driven by an optimal optical waveform. For an optimized laser pulse shape, strong constructive interference is obtained in the frequency domain between emissions from different electron trajectories, thereby selectively enhancing a particular harmonic order. This work demonstrates that coherent control in the strong-field regime is possible by adjusting the peaks of a laser field on an attosecond time scale.

Nonlinear optical effects due to the phase between carrier and envelope are observed with 5 fs pulses from a Kerr-lens mode-locked Ti:sapphire laser. These sub-two-cycle pulses with octave spanning spectra are the shortest pulses ever generated directly from a laser oscillator. Detection of the carrier-envelope phase slip is made possible by simply focusing the short pulses directly from the oscillator into a BBO crystal. As a further example of nonlinear optics with such short pulses, the interference between second- and third-harmonic components is also demonstrated.

Electromagnetic wave chaos is investigated using two-dimensional optical cavities formed in a cylindrical gradient refractive index lens with reflective surfaces. When the planar ends of the lens are cut at an angle to its axis, the geometrical ray paths are chaotic. In this regime, the electromagnetic mode spectrum of the cavity is modulated by both real and ghost periodic ray paths, which also “scar” the electric field intensity distributions of many modes. When the cavity is coupled to waveguides, the eigenmodes generate complex series of resonant peaks in the electromagnetic transmission spectrum.

We report experiments showing the breakup and the merging of filaments formed by the modulational instability of femtosecond optical pulses in air. For input powers as high as $25$ times the self-focusing threshold, the beams are shown to split into two spots, which coalesce into a self-guided beam. This effect occurs in an optically Kerr regime and plays an important role in the guiding process. Numerical simulations and theoretical estimates both support the comparison with the experimental data.

We predict the existence of stable nonlinear localized modes near the band edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr nonlinearity. Employing the technique based on the Green function, we reveal a physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystals.

Dynamical systems theory is used to construct a general phase-space version of transition state theory. Special multidimensional separatrices are found which act as impenetrable barriers in phase-space between reacting and nonreacting trajectories. The elusive momentum-dependent transition state between reactants and products is thereby characterized. A practical algorithm is presented and applied to a strongly coupled Hamiltonian.

We show that the transition from laminar to active behavior in extended chaotic systems can vary from a continuous transition in the universality class of directed percolation with infinitely many absorbing states to what appears as a first-order transition. The latter occurs when finite lifetime nonchaotic structures, called “solitons,” dominate the dynamics. We illustrate this scenario in an extension of the deterministic Chaté-Manneville coupled map lattice model and in a soliton including variant of the stochastic Domany-Kinzel cellular automaton.

We present the computer simulation results of a chain of hard-point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier’s law at the thermodynamic limit. This result is against the actual belief that one-dimensional systems with momentum conservative dynamics and nonzero pressure have infinite thermal conductivity. It seems that thermal resistivity occurs in our system due to a cooperative behavior in which light particles tend to absorb much more energy than the heavier ones.

We perform a systematic experimental study of the influence of the type of base on the avalanche dynamics of slowly driven 1D ball piles. The control of base details allows us to explore a wide spectrum of pile structures and dynamics. The scaling properties of the observed avalanche distributions suggest that self-organized critical behavior is approached as the “base-induced” disorder at the pile profile increases.

On the basis of deterministic fractals and the Rotne-Prager hydrodynamic interaction tensor, we confirm the asymptotic as well as the finite size scaling of the friction coefficient $\lambda$ of a self-similar structure. The fractal assembly is made of $N$ spheres with its dimension varying from $D<\mathrm{}1\mathrm{}$ to $D=3\mathrm{}$. The number of spheres can be as high as $N\sim O\left({10}^4\right)$. The asymptotic scaling behavior of the friction coefficient per sphere is $\lambda \sim N^{1/D-1\mathrm{}}$ for $D>\mathrm{}1\mathrm{}$, $\lambda \sim (\ln N{)}^{-1\mathrm{}}$ for $D=1\mathrm{}$, and $\lambda \sim N^0$ for $D<\mathrm{}1\mathrm{}$. The crossover behavior indicates that while in the regime of $D>\mathrm{}1\mathrm{}$ the hydrodynamic screening effect grows with the size, for $D<\mathrm{}1\mathrm{}$ it is limited in a finite range, which decays with decreasing $D$.

The axial symmetry of a familiar Penning trap is broken by adding the radial magnetic field of an Ioffe trap. Despite the resulting loss of a confinement theorem, stable orbits related to adiabatic invariants are identified, expressions are given for their frequencies, and resonances that must be avoided are characterized. It seems feasible to experimentally realize the new Penning-Ioffe trap to test these theoretical predictions. It also may be possible to simultaneously confine cold positrons and antiprotons in a Penning-Ioffe trap, along with any cold antihydrogen they may form.

The flow between two concentric cylinders, $V\left(r\right)$, is studied analytically and computationally for a fluid with stable axial density stratification. A sufficient condition for linear, inviscid instability is $d(V/r{)}^2/\mathrm{dr}<\mathrm{}0\mathrm{}$ (i.e., all anticyclonically sheared flows) rather than the Rayleigh condition for centrifugal instability, $d(\mathrm{Vr}{)}^2/\mathrm{dr}<\mathrm{}0\mathrm{}$. This implies a far wider range of instability than previously identified. The instability persists with finite viscosity and nonlinearity, leading to chaos and fully developed turbulence through a sequence of bifurcations. Laboratory tests are feasible and desirable.

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schrödinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general $N$-coupled nonlinear Schrödinger equations ( $N$-CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among the modes. We also analyze the various possibilities and conditions for such collisions to occur. Further, we report the significant fact that the various partially coherent solitons discussed in the literature are special cases of the higher order bright soliton solutions of the $N$-CNLS equations.

Stacking faults appear to be the most common type of defect in inverted opals which are good candidates for photonic crystals with absolute gaps in the visible range of light. In this Letter we present for the first time a systematic study of the effect of stacking faults on the optical properties of self-assembled photonic crystals, by means of large-scale transmittance calculations for macroscopic slabs of inverted opals with randomly distributed stacking faults. We show that frequency gaps, as seen in optical transmission experiments, will in general appear wider in the presence of stacking faults. We attribute the above to Anderson localization of light due to disorder.

We studied coherent backscattering (CBS) of light from opal photonic crystals with incomplete band gaps. We observed a dramatic broadening of the CBS cone for incident angles close to the Bragg condition in the crystals. We modify the conventional CBS theory to incorporate Bragg attenuation resulting from the photonic band structure. By fitting the CBS data with the modified theory, we extract both the disorder-induced light mean-free path and the Bragg attenuation length of the inherent opal photonic crystal.

Experiments to study the effect of acoustic forces on individual bubbles in shear flows have been carried out. In the system that we have used, the competition between acoustic and fluid dynamical forces results in a spiraling bubble trajectory. This dynamics is modeled by expressing the balance between Bjerknes and hydrodynamic forces in terms of an ordinary differential equation model, to which a separation of time scales is applied. The success of this model shows that the simple force-balance approach is still meaningful when bubbles are subjected to sound fields.

A second order phase transition is observed for the homogeneous cooling state of a heavy impurity particle in a granular fluid. The order parameter $\phi$ is the ratio of impurity mean square velocity to that of the fluid, with a conjugate field $h$ proportional to the mass ratio. A parameter $\beta$, measuring the fluid cooling rate relative to the impurity-fluid collision rate, is the analog of the inverse temperature. For $\beta <1\mathrm{}$ the fluid is “normal” with $\phi =0\mathrm{}$ at $h=0\mathrm{}$, as in the case of elastic collisions. For $\beta >1\mathrm{}$ an “ordered” state with $\phi \ne 0$ occurs at $h=0\mathrm{}$, representing an extreme breakdown of equipartition. Critical slowing and qualitative changes in the velocity distribution function near the transition are noted.

We report new measurements of mixing of passive temperature field in a turbulent flow. The use of low temperature helium gas allows us to span a range of microscale Reynolds number, $R_{\lambda }$, from 100 to 650. The exponents ${\xi }_n$ of the temperature structure functions $〈|\theta (x+r)-\theta \left(x\right){|}^n〉\sim r^{{\xi }_n}$ are shown to saturate to ${\xi }_{\infty }\simeq 1.45\pm 0.1$ for the highest orders, $n\sim 10$. This saturation is a signature of statistics dominated by frontlike structures, the cliffs. Statistics of the cliffs' characteristics are performed, particularly their widths are shown to scale as the Kolmogorov length scale.

We present the first measurements of anisotropic statistical fluctuations in perfectly homogeneous turbulent flows. We address both problems of intermittency in anisotropic sectors and hierarchical ordering of anisotropies on a direct numerical simulation of a three dimensional random Kolmogorov flow. We achieved an homogeneous and anisotropic statistical ensemble by randomly shifting the forcing phases. We observe high intermittency as a function of the order of the velocity correlation within each fixed anisotropic sector and a hierarchical organization of scaling exponents at fixed order of the velocity correlation at changing the anisotropic sector.