The distributions of the first-passage time for the Poisson random walk on a straight line (also known as the telegrapher random process) subject to a given number of reversals in the walk are obtained explicitly for both the starting directions. These distributions are then used to obtain, again explicitly, the corresponding distributions of the maximum of the walk, proving the conjecture by Orsingher [Stochastic Process. Appl. 34, 49 (1990)] for the one started moving to the right. The latter distribution leads to reinterpretation of Kac’s solution of the telegrapher equation.

We report observations of chaotic bursting in a fluid, a convecting layer of ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He. At an aspect ratio Γ=6.0 and Prandtl number Pr=0.3 we find intermittent bursts out of a fully developed chaotic state. Above the onset of bursting the average length of a burst-free region varies as (R-${\mathit{R}}_{\mathit{b}}$${)}^{\mathrm{-}\gamma }$ with γ=4.6. The average length of a burst varies as (R-${\mathit{R}}_{\mathit{b}}$${)}^{\mathrm{\delta }}$ with δ=2.0. A particularly novel state was seen for Γ=4.25 and Pr=0.12, where there occurs a reversible switching transition involving two chaotic attractors.

Optical phase-shift measurements are reported for a homeotropically aligned chiral nematic liquid crystal subject to an applied ac electric field E. A change in phase shift linear in E was observed, with a characteristic relaxation time τ≊0.01 s. The effect vanished for the nonchiral (racemic) version of the material. The data, taken together with the symmetry, are consistent with an electroclinic effect at the surface, such that the induced molecular tilt propagates elastically into the bulk.

The ground state of an electrorheological fluid is examined for high dielectric contrast (${\mathrm{\epsilon }}_{\mathit{p}}$/${\mathrm{\epsilon }}_{\mathit{f}}$→∞). In contrast to the result of Tao and Sun [Phys. Rev. Lett. 67, 398 (1991)] for the dipole limit, three structures are found to be degenerate: face-centered cubic, hexagonal close packed, and body-centered tetragonal. However, particle column surface energy favors the body-centered tetragonal structure, which has a lower surface energy per particle at the critical volume fraction of particles.

The free energy of a nematic film, placed between two isotropic media, does not depend on the azimuthal angle if the two interfaces are parallel. It is shown that in the general case of nonparallel bounding, a particular value of the azimuthal orientation is energetically preferable. The directions of this geometrically imposed easy axis and of the thickness gradient need not necessarily coincide. The geometrical anchoring may induce the twist deformations and force the nematic liquid crystal to behave like an optically active object.

We report an observation of a smectic-A–smectic-C–smectic-F (A-C-F) meeting point in a binary liquid-crystalline system. Detailed high-precision x-ray measurements enabled us to characterize the meeting point as a triple point, a point at which the three phases coexist. A direct consequence of this result is the existence of a tricritical point (TCP) on the A-C boundary. Contrary to the known results, the TCP appears despite a large temperature range for the A phase and the occurrence of a nematic phase at a higher temperature. Bearing in mind that F is a tilted hexatic phase, it is suggested that a possible reason for this behavior is the molecular-tilt field arising from the coupling between the tilt and the bond-orientational-order parameters.

We study the recently proposed nonlinear kinetic-growth model with surface relaxation for molecular-beam epitaxy in both two (2D) and three (3D) dimensions. We find that the dynamics of the equation without noise is nonlinearly unstable, in contrast to the dynamics of the Kardar-Parisi-Zhang equation. Because of the large fluctuation exponent in 2D, one important consequence is that there exists a strong-coupling regime where the interface develops a local divergence in finite time. For 3D or higher dimensions, the fluctuation is not strong enough to drive the system towards divergence, and the scaling is correctly given by renormalization-group calculations.

We investigated experimentally the dynamical hysteresis in a weakly ionized rf magnetoplasma system by varying the frequency of the triangular modulation of the amplitude of rf voltage. The modulation covered a region consisting of two cascaded hysteresis loops with four different states. The high-frequency modulations cause finite delays of the onsets of bifurcations in the hysteresis diagrams. Power-law dependence of the delay width of bifurcation on the modulation frequency was observed. The finite delay at the bifurcation makes the system bypass certain states in the modulation cycle as the frequency increases. The bypassing processes occur stochastically and the probability of bypassing increases with the modulation frequency. Mode-locking windows with finite width exist in the high-frequency regime.

We report an observation of energy-pooling collisions in a rare-earth-metal atomic element (Yb). The collisional process populates atomic states having different electronic configurations. Population transfer from closed inner-shell states to open ones is put in evidence, and its rate is comparable to the other observed collisional processes.

We study a system composed of N identical bosons interacting in three dimensions via attractive Yukawa pair potentials V(r)=-${\mathit{e}}^{\mathrm{-}\lambda \mathit{r}}$/r. Four approaches to the problem are related: the ‘‘equivalent two-body method,’’ translation-invariant Gaussian trial functions, collective field theory, and Hartree trial functions. Upper and lower energy bounds are given and are compared to some recent results which were obtained independently by an optimized Hartree method [M. Membrado, F. Pacheco, and J. Sañudo, Phys. Rev. A 39, 4207 (1989)]. In the pure gravitational limit λ→0 the N-body energy is determined for all N and all values of the coupling with an error of less than 7.2%.

The problem of determining a pure state vector from measurements is investigated for a quantum spin of arbitrary length. Generically, only a finite number of wave functions is compatible with the intensities of the spin components in two different spatial directions, measured by a Stern-Gerlach apparatus. The remaining ambiguity can be resolved by one additional well-defined measurement. This method combines efficiency with simplicity: only a small number of quantities have to be measured and the experimental setup is elementary. Other approaches to determine state vectors from measurements, also known as the ‘‘Pauli problem,’’ are reviewed for both spin and particle systems.

Newly developed methods for finding the semiclassical or WKB eigenvalues and eigenfunctions for vector wave fields are applied to spinning particles moving in central potentials subject to spin-orbit forces. The new methods are like the familiar Bohr-Sommerfeld or Einstein-Brillouin-Keller quantization methods for scalar wave fields, but involve additional issues relating to Berry’s phase, gauge structures, and monopolelike singularities. All these extra issues occur in the asymptotics of spin-orbit coupling. The role of angular momentum and conservation laws is particularly interesting, due to the role played by gauge fields in the classical-quantum correspondence. The work presented is a contribution to ongoing semiclassical studies of shell structure in nuclei and other fermion systems such as metal clusters, as well as an example of the general methods of semiclassical vector wave quantization.

A simple model having classical and quantum degrees of freedom is studied. In the presence of dissipation, and in the limit of strong coupling between classical and quantum variables and large separation between the corresponding time scales, collapse of the wave packet is demonstrated. The collapse appears as a phase transition below a certain critical temperature. When a sufficiently strong external ac magnetic field is added, the system becomes chaotic. Possible experimental realizations are discussed.

We have observed an effect known as a quantum eraser, using a setup similar to one previously employed to demonstrate a violation of Bell’s inequalities. In this effect, an interfering system is first rendered incoherent by making the alternate Feynman paths which contribute to the overall process distinguishable; with our apparatus this is achieved by placing a half wave plate in one arm of a Hong-Ou-Mandel interferometer so as to rotate the polarization of the light in that arm by 90°. This adds information to the system, in that polarization is a new parameter which serves to label the path of a given photon, even after a recombining beam splitter. The quantum ‘‘eraser’’ removes this information from the state vector, after the output port of the interferometer, but in time to cause interference effects to reappear upon coincidence detection. For this purpose, we use two polarizers in front of our detectors. We present experimental results showing how the degree of erasure (which determines the visibility of the interference) depends on the relative orientation of the polarizers, along with theoretical curves. In addition, we show how this procedure may do more than merely erase, in that the act of ‘‘pasting together’’ two previously distinguishable paths can introduce a new relative phase between them.

The self-field QED is based on a nonlinear action in the ψ field alone obtained by eliminating the electromagnetic field ${\mathit{A}}_{\mathrm{\mu }}$. This approach, previously applied to spontaneous emission, vacuum polarization, and g-2 and to the low-energy part of the Lamb shift, is here extended to the fully relativistic calculation of the Lamb shift. It is shown that, to first order of iteration, it gives the same result as the quantized theory of Mohr [Ann. Phys. (N.Y.) 88, 26 (1974); 88, 52 (1974)]. The renormalization procedure is different and simpler.

The harmonic-oscillator phase state that is subjected to a nonlinear evolution exhibits remarkable properties. The state evolves into a generalized phase state. A discrete superposition of distinct phase states can evolve, and one special state consists of a superposition of two phase states out of phase by π rad. The condition for the phase state to evolve into a finite superposition of phase states is intimately related to whether the scaled time of evolution is rational or irrational. The phase distribution for these phase states is presented, and ideal phase measurements of the evolved phase states are described. The diagonal elements of the nonlinear evolution operator in the phase-state basis are shown to be related to curlicues and Gaussian sums.

We have carried out precision calculations of various second-order sums for the two-electron positive ions ${\mathrm{Li}}^{+}$, ${\mathrm{Be}}^{2+}$, and ${\mathrm{B}}^{3+}$. These have the form ${\mathit{tsum}}_{\mathit{N}}$〈0‖V‖N〉〈N‖V‖0〉/(${\mathit{E}}_{\mathit{N}}$-${\mathit{E}}_0$${)}^{\mathit{k}}$, where k=1,2,3. The perturbation V is in each case a multipole-potential term, and for k=1 the sum corresponds to the usual definition of multipole polarizability. The initial state 0 and the intermediate states N are constructed from two-particle Hylleraas basis sets of the appropriate symmetry and angular momentum. Although the set N does not contain any true continuum functions, the pseudostates represent the continuum very well, and excellent convergence is obtained. These two-body quantities are then used to evaluate the energy levels of three-electron systems in high Rydberg states by the asymptotic-optical-potential method previously used for two-electron systems, retaining all terms up to order ${\mathit{x}}^{\mathrm{-}6}$. The results are good, but they can be still further improved by including higher-order terms, which will require multiple summation over intermediate states.

The natural lifetimes of the aluminum 3${\mathit{s}}^2$nl, n=3–12, l=0–3, have been calculated using wave functions that were obtained by direct numerical integration of the Schrödinger equation with a central potential to describe the ionic core and experimental term energies as input. The strong perturbation of the 3${\mathit{s}}^2$nd ${}_{}{}^2{}_{}{}^{}$D series by the yet to be experimentally identified 3s3${\mathit{p}}^2$ ${}_{}{}^2{}_{}{}^{}$D perturber has been explicitly treated semiempirically by using experimental mixing coefficients. Inclusion of at least this perturbation is essential for good agreement with experiment. The effects of blackbody radiation are also explicitly included and have a dramatic effect on the lifetimes of the np states. Core-polarization effects are also included in the transition matrix elements.

Dynamic polarizabilities of halide and ${\mathrm{H}}^{\mathrm{-}}$ ions are computed by applying dispersion relations to photodetachment cross sections. Recent calculations of photodetachment cross sections using the relativistic random-phase approximation were used for the halides ${\mathrm{F}}^{\mathrm{-}}$, ${\mathrm{Cl}}^{\mathrm{-}}$, ${\mathrm{Br}}^{\mathrm{-}}$, and ${\mathrm{I}}^{\mathrm{-}}$. The bound-state to free-state absorption coefficient of ${\mathrm{H}}^{\mathrm{-}}$ evaluated previously using a set of successively improved bound- and free-state wave functions was used to obtain the polarizability of ${\mathrm{H}}^{\mathrm{-}}$. The ${\mathrm{H}}^{\mathrm{-}}$ result is compared with other recent theoretical calculations. Results for the static polarizabilities α(ω=0) are compared with other theoretical techniques and experiment.

The ionization potentials of lithiumlike 1${\mathit{s}}^2$2s states are calculated for systems with nuclear charge Z=11 to 20 using a full-core plus correlation method. The relativistic corrections are included using first-order perturbation theory. The QED contributions to the ionization potential are calculated using effective nuclear charge. These results are compared with data available in the literature.