The analogy between quantum tunneling of particles and evanescent electromagnetic waves can be used to study particle tunneling. Possibilities for the measurement of the time delay resulting from the transmission of waves through an evanescent region, say with lower dielectric constant, are discussed. In contrast to particle tunneling, an electromagnetic pulse can consist of many photons and can be probed in a noninvasive way. We emphasize the delay of the centroid of an electromagnetic pulse transmitted below cutoff through a portion of a waveguide with the same cross section as the adjacent propagating guides. The boundary conditions at the interface between the propagating and the evanescent region lead to the same transmission and reflection coefficients as for a square-barrier tunneling problem. For a pulse restricted to a narrow frequency range, the time delay depends only on the frequency derivative of the phase shift associated with transmission. The delay of a centroid is just that; there is no deeper physical sense which links the incoming centroid to the outgoing centroid. For sufficiently long evanescent regions, the delay is independent of thickness.

A practical example, which admits a fully exact solution, is presented and then employed to study adiabaticity. The example consists of an oscillator whose oscillation frequency changes at a finite rate within a finite time interval. An analytically exact formula is given for the adiabatic ratio, which is a good measure of the adiabaticity. General and practical features of the adiabaticity, including the adiabatic theorem, are presented.

We start with a succinct presentation of the nonhomogeneous nondispersive waves and different covariant formalisms of electromagnetism. Then, using traceless second-rank spinors, we show that it is easy to infer the nonhomogeneous nondispersive electromagnetic waves from the scalar ones. Finally, we discuss the global and local behavior of these waves and their physical properties.

We present an analytical technique for counting exactly the number of ways of embedding a graph in a fairly general family of self-similar deterministic fractals. As a result, series expansion for statistical systems can be obtained that are exact order by order in the expansion parameter. As an illustration, series expansions for self-avoiding walks on a Sierpriaanski carpet are given. Analytical results for systems on infinitely ramified fractals are obtained in the thermodynamic limit without making any approximation on the lattice.

For trace maps associated with general substitution rules involving two-letter matrices A and B, it has been conjectured that the quantity I=1/2 Tr([A,B${]}^2$) transforms as I’=P(x,y,z)I, where x, y, and z are the traces of A, B, and AB, respectively. By expressing the transformed matrices A’ and B’ as linear combinations of A, B, AB, and the identity matrix, the conjecture is proved.

Microwave-scattering studies help to establish a link between classical chaos and the corresponding quantum dynamics. We present an analysis of recent experimental data using a theory based on random matrices that takes full account of quantal aspects and compare the results with the semiclassical approach. In our analysis purely wave-mechanical effects are seen, namely a non-Lorentzian correlation of the frequency spectrum, leading to a nonexponential decay in time.

An additional potential objection is noted to the recent argument that the Nernst-Simon and unat- tainability statements of the third law of thermodynamics are not equivalent, but rather make independent assertions about the kinds of the Hamiltonians found in nature. Although valid in a limited sense, the objection does not invalidate the conclusions reached there and illustrates several significant points about the importance of the thermodynamic limit in considerations of the third law.

Nodal patterns of stationary capillary waves formed on the surface of water enclosed in an agitated ripple tank with circular and stadium-shaped cylindrical walls are examined in the low-frequency (ν<50 Hz) and high-frequency (ν>700 Hz) regimes. In the low-frequency regime, in agreement with predictions of quantum-chaos theory, the shape of the tank’s boundaries (integrable or nonintegrable) dictates the type of nodal patterns obtained. In the high-frequency regime we obtain nodal patterns characterized by short-range order (called ‘‘scarlets’’ because they are believed to be the precursors of quantum scars), as recently predicted in the quantum-chaos context by P. O’Connor, J. Gehlen, and E. J. Heller [Phys. Rev. Lett. 58, 1296 (1987)].

We calculate, for a spin-1/2 Ising model within the mean-field approximation, the line tension along partial-wetting surface states up to a first-order wetting transition where the line disappears. We likewise calculate the line tension of the boundary between the two coexisting surface states at the prewetting transition and follow its behavior into the neighborhood of bulk wetting. In both cases we find evidence for the divergence of the line tension.

Angular-differential cross sections for charge transfer with simultaneous emission of a photon in collisions of protons with helium atoms have been measured. The incident proton energies were 25, 50, and 100 keV and the center-of-mass scattering angles were between 0 and 2.0 mrad. In the experiment, hydrogen atoms that scattered through an angle θ were detected in coincidence with photons emitted perpendicular to the scattering plane with a wavelength between 1140 and 1400 Å. Differential cross sections for capture into the 2p state of the hydrogen atom were determined from the variation in the coincidence signal with θ. The experimental results are compared with the results of a classical trajectory Monte Carlo (CTMC) simulation and with the results of a calculation for H(2p) capture using the Coulomb-Brinkman-Kramers (CBK) approximation. The agreement between the experimental results and the CTMC calculation is good at all three energies while the agreement between the shape of the data and the CBK calculation is good at 50 and 100 keV.

The LMM dielectronic recombination resonances of a neonlike ion (${\mathrm{Au}}^{69+}$) have been observed. The ions were produced and held in an electron-beam ion trap. The intensity of the n=3→2 x rays resulting from dielectronic recombination was measured as a function of electron-beam energy with sufficient resolution to distinguish the structure of the LMM resonances. The measured resonance strengths for LMM resonances with a 2${\mathit{p}}_{3/2}^{\mathrm{-}1}$ core are in good agreement with theoretical predictions, but there is some disagreement for the 2${\mathit{p}}_{1/2}^{\mathrm{-}1}$ and 2${\mathit{s}}_{1/2}^{\mathrm{-}1}$ core configurations.

Complete molecular valence-electron spectra were measured for CO. Unexpectedly, discrete lines at low kinetic energies were found, superimposed on a continuous energy spectrum representing direct double-ionization processes. The appearance of these lines is discussed in the context of the formation of the ${\mathrm{C}}^{+}$+${\mathrm{O}}^{+}$ ion pair near its associated threshold at 38.4 eV. It is ascribed to valence-excited repulsive (${\mathrm{CO}}^{+}$${)}^{\mathrm{*}}$ states, which dissociate to a large part rapidly into atomic fragments before electronic relaxation takes place. From our spectra, partial cross sections for the different processes leading to dissociative valence double ionization are derived.

We investigate the convoy-electron (CE) emission produced during grazing bombardment of a Cu(100) surface with 20–100-keV protons. At 0.5° of incidence the CE peak measured at projectile energies below 50 keV along the direction of specular reflection of the ions presents the same width and shape as the CE peak corresponding to ${\mathrm{H}}^{+}$-He collisions and is considerably narrower than that observed in transmission through thin foils. This finding shows that CE’s are mainly subjected to the Coulomb potential of the scattered ion when the velocity resolutions are high enough to localize electron states close to the ion velocity. A strong variation of the CE peak shape with the projectile incidence angle was also observed. This finding can be explained by a calculation that takes into account the angular distribution of the reflected ions.

In a two-component gas consisting of light-absorbing particles immersed in a buffer gas, velocity-selective excitation combined with a state-dependent kinetic collision frequency results in light-induced drift. Standard theory predicts that the drift velocity as a function of frequency detuning should have a dispersion-curve-like behavior. This was indeed found experimentally for the molecular species studied so far. We report a dramatic deviation from this behavior for ${\mathrm{C}}_2$${\mathrm{H}}_4$, excited into its ${\nu }_7$ vibrational mode by a ${\mathrm{CO}}_2$ laser, with Kr as a buffer gas. The extent of the deviation is found to depend strongly upon the rotational sublevels involved. A possible explanation in terms of a three-level model is attempted but found to be unlikely.

We numerically solve the Cahn-Hilliard equation in two dimensions for very large system sizes and for two different values of the volume fraction φ. We present results for the scaling function of the droplet distribution function and compare it with several different theoretical predictions. We find that for φ=0.05 the agreement between simulation results and recent theoretical predictions are reasonably good, while none of the existing theories seem to agree well with the simulation data for φ=0.21.

We study the effect of quenched disorder on the behavior of tethered membranes using both analytic and numerical methods. Disorder is introduced via a random spontaneous curvature and a random preferred metric. The presence of impurity-induced spontaneous curvature is found to stiffen the long-wavelength bending rigidity, stabilizing a new disordered flat phase at temperature T=0. This new phase, like that of pure membranes at T>0, is characterized by anomalous statistical and elastic properties. Since its origin is purely mechanical, it can, in principle, be constructed from an appropriate array of macroscopic springs.

The asymptotic large-behavior of the saturation coverage in multilayer deposition without screening is studied by analytical considerations and numerical Monte Carlo simulations. It is argued that the convergence law to the limiting coverage is related to the problem of the random-walk survival probability on a lattice with a partial trap at the origin. A model is introduced that has a logarithmic, rather than power-law, asymptotic coverage behavior, confirmed by numerical results.

Precisely at a critical undercooling ${\mathrm{\Delta }}_{\mathit{c}}$, one-dimensional solidification fronts can travel with a velocity v, which scales in time as ${\mathit{t}}^{\mathrm{-}1/3}$. This result, recently found in computer simulations and explained on dimensional grounds, is derived here from the starting equations.

As an experimentally realizable two-dimensional fluid system, we perform a cell-dynamical system simulation of a binary incompressible fluid that undergoes spinodal decomposition after a critical quench in a Hele-Shaw cell. Fluidity enhances fluctuations of interfaces, resulting in a form factor that continuously depends on the fluidity of the system. In this system, finite size coupled with the effect of incompressible flow is found to have a severe accelerating effect on the growth law.