We reply to the Comment by Knipp [Phys. Rev. A 41, 4547 (1990)]. We show that Knipp’s proposal for the dynamical structure factor S(k,ω) should be extended away from long wavelength by a suitable choice of γ(k) generalizing the ratio of the specific heats γ==γ(0). The choice γ(k)=${\mathit{B}}_{\mathit{S}}$(k)/${\mathit{B}}_{\mathit{T}}$(k) leads back to our original proposal for the dispersion relation of the collective mode in a liquid metal like Rb, ${\mathit{B}}_{\mathit{S}}$ and ${\mathit{B}}_{\mathit{T}}$ being adiabatic and isothermal bulk moduli.

The general conclusions of the recent article by Andrews and Blake [Phys. Rev. A 38, 3113 (1988)] on the forbidden nature of higher-order multipolar contributions to optical second-harmonic generation are misleading and not generally valid.

The preceding Comment [Phys. Rev. A 41, 4549 (1990)] by Zhu and Shen is incorrect on a number of issues.

We describe simple, stable, and economical numerical methods for implementing temperature and pressure controls in equilibrium and nonequilibrium Nosé-Hoover dynamics. These methods substantially increase the efficiency of large-scale simulations.

By comparing some of the problems of self-avoiding walks (SAWs) on critical percolation clusters (CPCs) to those of random walks, specific issues that need classification in order to understand the critical behavior of SAWs on CPCs are considered. From these issues and the node-link-blob picture of CPCs we discuss crossover scaling theory and the universality of SAWs on CPCs. Recent simulation results are also considered.

We investigate the current flow under anomalous-diffusion conditions (disordered media and also turbulent motion) in the limit of strong-bias fields. A unified picture for anomalous behavior is provided by Lévy walks. These are continuous-time random walks with coupled spatial and temporal memories. We find that the long-time asymptotic behavior of the current adheres to the following power laws: dispersive transport decreasing and enhanced diffusion increasing with time. In both cases the characteristic exponents depend (in a complex way) on the memory terms. We corroborate the values of the exponents by Monte Carlo simulations.

We propose to characterize strong disorder and the degree of disorder (in anomalous diffusion problems) by the divergence and the divergence law, respectively, of the mean first passage time to leave an arbitrary interval of finite size. Exact results for the exponents and amplitudes characterizing the divergence are given for certain models.

The wake of a pair of identical cylinders placed side by side in a uniform flow is visualized. Different flows appear when the distance between the cylinders is decreased. For large gaps, the study of the phase difference between the vortex shedding shows that locking occurs and can be associated with asymmetric flows. For small gaps, a new vortex pattern with a separated stagnant zone is visualized. Finally, a classical alternate vortex street is observed at very small gaps. An analogy with coupled oscillators is then presented in order to interpret the asymmetric regimes as beats between the wakes.

A different approach to study the viscosity of concentrated suspensions is proposed. It is based on percolation theory. It is suggested that at the critical concentration of fillers, ${\mathrm{\phi }}_{\mathit{c}}$ a macroscopic interconnected cluster (secondary structure) of fillers is formed. This cluster extends from one wall of the rheometer to the other. It is the properties of this macroscopic cluster which determine the viscosity for φ≥${\mathrm{\phi }}_{\mathit{c}}$. An analytic formula is derived for ${\mathrm{\eta }}_{\mathit{r}}$(φ) above ${\mathrm{\phi }}_{\mathit{c}}$, which is tested against a number of sets of experimental data.

Unbinding transition of fluid and polymerized membranes are studied by renormalization-group (RG) methods. Two different RG schemes are used and found to give rather consistent results. The fixed-point structure of both RGs exhibits a complex behavior as a function of the decay exponent τ for the fluctuation-induced interaction of the membranes. For τ>${\mathrm{\tau }}_{\mathit{S}2}$, interacting membranes can undergo first-order transitions even in the strong-fluctuation regime. Our estimates for ${\mathrm{\tau }}_{\mathit{S}2}$ imply, however, that both fluid and polymerized membranes unbind in a continuous way in the absence of lateral tension.

We consider the impact of shear flow on the isotropic-nematic transition in crystalline liquids by generalizing Leslie-Ericksen dynamics of nematic systems to include amplitude and biaxial degrees of freedom. Neglecting fluctuations, we find steady-state solutions to the equations of motion for the nematic order parameter and fluid velocity and interpret them in terms of nonequilibrium steady states. We predict a transition temperature increasing with shear rate up to a nonequilibrium critical point, and discuss the singular behavior of the order parameter and external stress near this point.

We present two methods for a direct Monte Carlo evaluation of the surface entropy ${\mathit{S}}_{\mathit{s}}$ of a liquid interacting by specified, volume-independent potentials. The first method is based on an application of the approach of Ferrenberg and Swendsen [Phys. Rev. Lett. 61, 2635 (1988); 63, 1195 (1989)] to Monte Carlo simulations at two different temperatures; it gives much more reliable results for ${\mathit{S}}_{\mathit{s}}$ in liquid Si than previous calculations based on numerical differentiation. The second method expresses the surface entropy directly as a canonical average at fixed temperature.

The bond-length and bond-angle distributions in dense two-dimensional liquids exhibit distinct multiple peaks that arise from a local geometrical structure that resembles plane tilings of squares and equilateral triangles. The structure of the dense two-dimensional liquid can be described as a square-triangle tiling containing numerous low-strength tiling faults. These observations suggest a novel geometrical mechanism for two-dimensional melting.

We propose a position-space renormalization-group approach to the problem of viscous fingering in the absence of surface tension, with arbitrary viscosity ratio between the injected and displaced fluid. We find there are only two fixed points, the Eden and the diffusion-limited aggregation (DLA) points. The Eden point, which corresponds to a compact cluster with nonfractal surface, is stable in all directions, while the DLA fixed point is a saddle point. Hence if the viscosity of the injected fluid is not zero, the system must eventually cross over to a compact cluster. We also calculate the crossover exponent φ and crossover radius ${\mathit{R}}_{\times }$, and discuss possible experimental measurements.

The transmission coefficient for electrons incident on an oscillating thin potential barrier is calculated for the case of a classical barrier and for the case where phonons are present (quantum barrier). In the classical case we find a feedback mechanism between elastic and inelastic tunnel current similar to that found by Gelfand, Schmitt-Rink, and Levi [Phys. Rev. Lett. 62, 1683 (1989)] in the quantum barrier case.

We continue with our series of papers concerning a self-field approach to quantum electrodynamics that is not second quantized. We use the theory here to show that a detector with a uniform acceleration a will respond to its own self-field as if immersed in a thermal photon bath at temperature $T_a$=ħa/2πkc. This is the celebrated Unruh effect, and it is closely related to the emission of Hawking radiation from the event horizon of a black hole. Our approach is novel in that the radiation field is classical and not quantized; the vacuum field being identically zero with no zero-point energy. From our point of view, all radiative effects are accounted for when the self-field of the detector, and not the hypothetical zero-point field of the vacuum, acts back on the detector in a quantum-electrodynamic analog of the classical phenomenon of radiation reaction. When the detector is accelerating, its transformed self-field induces a different back reaction than when it is moving inertially. This process gives rise to the appearance of a photon bath, but the photons are not real in the sense that the space surrounding the accelerating detector is truly empty of radiation, a fact that is verified by the null response of an inertially moving detector in the same vicinity. The thermal photons are in this sense fictitious, and they have no independent existence outside the detector.

We use a self-field approach to quantum electrodynamics (QED) to show how one may obtain spontaneous emission and the Lamb shift in a two-level atom without second quantization of the radiation field. In addition, we compare the self-field formalism to that of the neoclassical theory of electrodynamics advanced by Crisp and Jaynes [Phys. Rev. 179, 1253 (1969)]. We show that the neoclassical model can be obtained from the self-field approach used here, but that the two are not equivalent. In particular, the self-field approach appears to give a more complete description of radiative processes. Finally, we show that the neoclassical theory’s prediction of a nonexponential ‘‘chirruped’’ decay is most likely a mathematical artifact of the improper application of the superposition principle in a nonlinear model where such a principle does not hold. A correct treatment with self-field QED yields the usual exponential decay dynamics.

The quantum Zero effect is the inhibition of transitions between quantum states by frequent measurements of the state. The inhibition arises because the measurement causes a collapse (reduction) of the wave function. If the time between measurements is short enough, the wave function usually collapses back to the initial state. We have observed this effect in an rf transition between two ${}_{}{}^9{}_{}{}^{}$${\mathrm{Be}}^{+}$ ground-state hyperfine levels. The ions were confined in a Penning trap and laser cooled. Short pulses of light, applied at the same time as the rf field, made the measurements. If an ion was in one state, it scattered a few photons; if it was in the other, it scattered no photons. In the latter case the wave-function collapse was due to a null measurement. Good agreement was found with calculations.

The explicit coordinate representation of coherent states for the Morse oscillator is derived and discussed, in the limit that the potential well is deep. Without this limit, such states can only be written as a finite sum that does evolve coherently but in a dilated time.

We study the nature of the quasienergy spectrum of the quantum version of the Fermi-accelerator model consisting of a particle inside a box with one fixed and one oscillating wall.