The stationary problem of a one-dimensional wave transition through a fat-fractal slab is considered in the small-wavelength limit. The convergence of the numerical approach is discussed. An analysis of the accuracy of the calculation yields the conditions that allow one to approximate an authentic fractal layer by a structure obtained with a finite number of steps. This number decays exponentially with the incident wavelength.

It is argued that a recently proposed algorithm [K.Y.R. Billah and M. Shinozuka, Phys. Rev. A 42, 7492 (1990)] for the integration of stochastic differential equations in the presence of correlated noise does not introduce a substantial improvement over existing schemes. We point out that although this scheme could be very interesting for noise characterized by particular correlation functions, for colored noise the present scheme is sensibly slower than existing algorithms. Some apparent discrepancies between the result of simulations carried out with the new algorithm and previous numerical work are explained.

In the preceding Comment [Phys. Rev. A 46, 8028 (1992)], Mannella and Palleschi critique the power spectral density method of colored-noise generation and its application to the bistable potential [Phys. Rev. A 42, 7492 (1990)]. These writers make a critical analysis of the outlined advantages of the method and compare it to the stochastic differential equation approach. A reply to the Comment is given based on the work that was presented without adding any new results. It is emphasized that the primary intent of the original paper was to present an option for generating colored noise for use in many statistical physics problems.

Interactions between target and projectile electrons leading to ionization of one of the collision partners and simultaneous excitation of the other are investigated for fast clothed-particle–clothed-particle collisions. For H-atom impact, the first Born approximation is used to demonstrate that the low-energy-electron emission is dominated by electron-electron rather than by electron-nucleus interaction processes. For a broad class of structured particle collision systems, the electron-electron interaction is shown to play an important, non-neglibible, role. Doubly differential cross sections for energetic H-He collisions illustrate this point.

A formulation for calculating the distorted-wave Born approximation cross sections for both atomic and molecular ionizations using the partial-wave-expansion method is introduced. The ionization cross sections of molecular and atomic hydrogen target with positron impact are calculated in the intermediate collision velocity region with this formulation. The results are compared to the updated experiment data. This comparison has offered an alternative evaluation for the present model of ionization process.

Planar quadrupole ion traps have been analyzed through numerical and analytic solutions of Laplace’s equation. These involve either one or more conducting rings or their analogs, a hole in one or more conducting sheets. The leading terms in the potential are harmonic, corresponding to the Paul trap, but with coefficients that reduce their efficiency and for some traps, the anharmonic terms can be suppressed to eighth-order. Stable ion trapping is predicted for all electrode configurations possessing radial and axial symmetry. A three-hole microtrap with an inner hole radius of 80 μm trapped from one to many (dense clouds) laser-cooled ${\mathrm{Ba}}^{+}$ ions where the two-ion distance is compressed to 1 μm, allowing new experiments in quantum optics. Also, arrays of traps for optical clocks are contemplated using photolithographic fabrication.

Although the two-photon spontaneous emission is electric dipole forbidden, there is a two-photon stimulated emission whose lifetime is much longer in comparison to those of excitations spontaneously emitted by the excited states of the atom. Conditions are established under which the two-photon stimulated emission prevails, indicating that significant amplification is likely to occur near the two-photon frequency.

The techniques of electron-electron and electron-ion covariance mapping have been used to confirm that a laser of modest rise time (∼1 ps) and focused intensity (∼${10}^{15}$ W/${\mathrm{cm}}^2$) will doubly ionize ${\mathit{H}}_2$ molecules in a sequential manner. This stepwise behavior manifests itself in structureless features on the electron-electron maps. However, the technique can be employed to search for correlated emission of two or more electrons in more complex systems. Electron-ion maps, on the other hand, can apportion the electrons in a typical photoelectron spectrum to the parent ions and to fragment ions of all energies.

We show that the use of weakly probed three-level atoms in the Λ configuration as a nonlinear medium inside an optical cavity enables the almost lossless transformation of an incoming strong coherent light beam into an outgoing amplitude-squeezed light beam.

We investigate the quantum-mechanical noise in spectroscopic experiments on ensembles of N two-level (or spin-1/2) systems where transitions are detected by measuring changes in state population. By preparing correlated states, here called squeezed spin states, we can increase the signal-to-noise ratio in spectroscopy (by approximately ${\mathit{N}}^{1/2}$ in certain cases) over that found in experiments using uncorrelated states. Possible experimental demonstrations of this enhancement are discussed.

Under conditions of strong dipole coupling an optical cavity containing one atom behaves as a two-state system when excited near one of the ‘‘vacuum’’ Rabi resonances. A coherent driving field induces a dynamic Stark splitting of the ‘‘vacuum’’ Rabi resonance. We demonstrate this two-state behavior in computer experiments based on quantum trajectory simulations.

We study field-theoretic A+A→0/ in a perturbative renormalization-group framework. We calculate the reacted fraction and it is shown that, in addition to the reaction coupling constant, a second ‘‘crossover’’ parameter must be treated to all orders to obtain meaningful long-time results for spatial dimensions d≤2. At d=2 the result is consistent with known rigorous long-time bounds, but the short-time behavior remains inconsistent (trivial) analogously to the Landau ghost of QED and ${\mathrm{\phi }}^4$ theory. We argue that this inconsistency is true to all orders in the coupling constants.

A discrete version of the complex Ginzburg-Landau equation is studied on a completely connected lattice of N sites. This can equivalently be described as a model of N identical globally coupled limit-cycle oscillators. The phase diagram is obtained by a combination of numerical and analytical techniques. A surprising variety of dynamical behaviors is found in the thermodynamic limit (N≫1). Depending on the region of parameter space, one gets the following: (1) a simple homogeneous limit cycle; (2) a state with complete frequency locking but with no phase locking so that the global forcing term vanishes; (3) a breaking of the system into a few macroscopic clusters which can exhibit periodic or quasiperiodic dynamics; (4) surprisingly complex states where an individual oscillator behaves in a chaotic way but in a sufficiently coherent manner so that the average complex amplitude does not vanish in the thermodynamic limit. Moreover, in this last region, the dynamics of this natural order parameter is itself chaotic.

Extensive numerical simulations of the discretized one-dimensional Kuramoto-Sivashinsky interface equation, in conjunction with a detailed crossover analysis, indicate that the large-scale fluctuations of this deterministic chaotic system are described by the noisy Burgers equation. As a consequence of a large effective interfacial tension, the asymptotic behavior is observed only after a long intermediate scaling regime. The skewness of the interfacial fluctuations is found to be a useful probe of the crossover.

An escape mechanism in a bistable system driven by colored noise of large but finite correlation time (τ) is analyzed. It is shown that the fluctuating potential theory [Phys. Rev. A 38, 3749 (1988)] becomes invalid in a region around the inflection points of the bistable potential, resulting in the underestimation of the mean first passage time at finite τ by this theory. It is shown that transitions at large but finite τ are caused by noise spikes, with edges rising and falling exponentially in a time of O(τ). Simulation of the dynamics of the bistable system driven by noise spikes of the above-mentioned nature clearly reveal the physical mechanism behind the transition.

We investigate the synchronization between two systems consisting of coupled circle maps that have a common drive, which may be chaotic or regular. We observe several new aspects of chaotic and regular synchronization. In the chaotic regime the transition from synchronization to nonsynchronization corresponds to the transition from one to two positive Liapunov exponents. We find regions in the parameter space with periodic motion where synchronization is always achieved, never achieved or, depending on the initial conditions, sometimes achieved. The nonsynchronization or synchronization are stable in the presence of a weak chaotic (or noisy) signal.

We discuss the relation between scaling laws and dynamical behavior for earthquakes in the framework of a Burridge-Knopoff model. Due to the nontrivial interaction among many degrees of freedom, a new type of strongly intermittent chaos is found. The dynamics is dominated by wild fluctuations, implying exponential tails in the probability distributions. This is caused by very slow relaxation of time correlations, which gives rise to an anomalous behavior for the effective Lyapunov exponent and for the time signal of the earthquake magnitude.