We compare two dynamical mean-field theories for the calculation of the dielectric response function ε(kω) of a strongly coupled Coulomb liquid. The two approximations share the feature that they express the correlational part of the linear response function in terms of the quadratic response function. We point out that even though the two approaches, the velocity-average approximation of Golden and Kalman [Phys. Rev. A 19, 2112 (1979)] and the universal mean-field approximation of Tao and Kalman [Phys. Rev. A 43, 973 (1990)], start from entirely different premises, they lead to the same result as to how the linear and quadratic response functions are related. On the other hand, they ultimately differ from each other in the way they break up the quadratic response function in order to achieve self-consistency.

The coefficient of the von Weizsäcker term in the Thomas–Fermi–von Weizsäcker energy functional is determined within a perturbation framework for high-temperature plasmas. A notable deviation in comparison to the corresponding zero-temperature result is found.

The cross-spectral-density function characterizing a general propagation-invariant wave field satisfies the associated (planar) paraxial equation. Building on this result, we solve exactly the problem of the passage of such fields through arbitrary lossless optical systems characterized by their ABCD matrices. It is shown that the wave field remains shape invariant in all such systems, but that the property of strict propagation invariance is conserved only if the system is afocal.

We study the retrieval properties of an extremely diluted neural network with multispin interactions. We calculate the phase diagram and show that a retrieval phase appears through a first-order phase transition provided the interactions are of order greater than 2.

The double-layer impedance at a rough electrode can be related to properties of random walks near the surface of that electrode. We apply this method to the calculation of the double-layer impedance at a self-similar electrode in two dimensions. We find that the impedance at a self-similar surface shows stretched-exponential behavior. At high frequencies, this behavior is similar to the experimentally observed constant phase-angle behavior, with an exponent determined by the multifractal properties of the surface.

We examine how the size of a sandpile can affect the nature of the avalanches occurring on its surface. We propose a simple explantion for why, if a pile is made sufficiently small, the distribution of avalanches changes from what is observed in large systems and give a criterion for how small the pile must be in order for this to happen. This explanation does not support the conclusion that avalanches show self-organized critical behavior. We also present data which indicate that the distributions of avalanches in very narrow sandpiles are qualitatively the same as those found in large piles.

For directed percolation, the second nontrivial eigenvalue of the transfer matrix is shown to have its maximum at ${\mathit{p}}_{\mathit{c}}$. Using this, we obtain for (1+1)-dimensional directed site percolation ${\mathit{p}}_{\mathit{c}}$=0.706 522±0.000 005, which agrees within ${10}^{\mathrm{-}3}$ with other results, but is nevertheless significantly (in terms of quoted uncertainties) different from them. We also relate other quantities to the transfer-matrix spectrum and eigenfunctions.

The generalized hydrodynamics of two-dimensional lattice-gas automata is solved analytically in the linearized Boltzmann approximation. The dependence of the transport coefficients (kinematic viscosity, bulk viscosity, and sound speed) upon wave number k is obtained analytically. Anisotropy of these coefficients due to the lattice symmetry is studied for the entire range of wave number, k. Boundary effects due to a finite mean free path (Knudsen layer) are analyzed, and accurate comparisons are made with lattice-gas simulations.

Spatially confined states of traveling-wave convection of arbitrary length are studied in ethanol-water mixtures contained in a narrow annular channel, a geometry that approximates a one-dimensional system with periodic boundary conditions. The measured properties of these states, including the Rayleigh number at which they are observed, the frequency and wave number of the traveling waves, and the spatial variation of the amplitude and wave number, are in agreement with recent numerical calculations, leading to a microscopic understanding of these dynamical, nonequilibrium structures.

By comparison of measurements of shadowgraph images of convection in ethanol-water mixtures with the results of recent numerical calculations, we study the role of the concentration field in traveling-wave and stationary convection. The results confirm the existence of a large concentration contrast between adjacent traveling-wave convection rolls. This concentration modulation, which decreases as the Rayleigh number is increased and the transition to stationary convection is approached, is fundamental to the translation of the pattern.

The effective response time ${\mathrm{\tau }}_{\mathrm{eff}}$ of the nematic-electroclinic effect was determined as a function of driving frequency and temperature. Near the nematic–smectic-A transition temperature ${\mathit{T}}_{\mathit{N}–\mathrm{Sm}\mathrm{-}}$A, ${\mathrm{\tau }}_{\mathrm{eff}}$ was found to be a function of driving frequency, indicating the existence of more than one physical process. Several degrees above ${\mathit{T}}_{\mathit{N}–\mathrm{Sm}\mathrm{-}}$A, ${\mathrm{\tau }}_{\mathrm{eff}}$ was found to be frequency independent up to 100 kHz. At these temperatures, moreover, the effective response times are quite small, of order 100 ns.

We study a variant of the Zhang model [Y.-C. Zhang, J. Phys. (Paris) 51, 2113 (1990)], ballistic deposition of rods with the length l of the rods being chosen from a power-law distribution P(l)∼${\mathit{l}}^{\mathrm{-}1\mathrm{-}\mathrm{\mu }}$. Unlike in the Zhang model, the site at which each rod is dropped is chosen randomly. We confirm that the growth of the rms surface width w with length scale L and time t is described by the scaling relation w(L,t)=${\mathit{L}}^{\mathrm{\alpha }}$w(t/${\mathit{L}}^{\mathrm{\alpha }/\mathrm{\beta }}$), and we calculate the values of the surface-roughening exponents α and β. We find evidence supporting the possibility of a critical value ${\mathrm{\mu }}_{\mathit{c}}$≊5 for d=1 with α=1/2 and β=1/3 for μ>${\mathrm{\mu }}_{\mathit{c}}$, while for μ<${\mathrm{\mu }}_{\mathit{c}}$, α and β vary smoothly, attaining the values α=β=1 for μ=2.

The nondecay probability Q(t) for a Lorentzian energy distribution peaked at ${\mathit{E}}_0$ with full width at half maximum equal to Γ is given in atomic units by ${\mathit{Q}}_{\mathit{L}}$(t)=exp(-Γt). However, the Lorentzian distribution includes energies in the range -∞≤E≤∞. On physical grounds, this distribution must be truncated at some minimum energy E=0. In this paper, Q(t) is derived for a properly normalized truncated Lorentzian energy distribution. To aid the analysis, the average lifetime τ(${\mathit{t}}_{\min }$) for that fraction of the system that has not decayed by ${\mathit{t}}_{\min }$ is also calculated for this system. For a given value of the ratio ${\mathit{E}}_0$/Γ, the function Q(t) shows different behavior in different time regimes; this behavior is presented and the time periods are determined. It is shown that Q(t) falls off linearly at very small t, but at a rate only half as fast as for ${\mathit{Q}}_{\mathit{L}}$(t). Thus this system cannot exhibit the behavior known as Zeno’s paradox, but rapid measurements on this system that collapse the wave function back to the original state could, in principle, reduce the decay rate by a factor of 2.

Electron mass renormalization and the Lamb shift have been investigated using the dispersion self-energy formalism. If shifts of both the electromagnetic field and quantum-mechanical transitions frequencies are considered, absorption from the electromagnetic field is canceled by emission due to atomic fluctuations. The frequencies of all modes are obtained from the self-consistency condition that the field seen by the electron is the same as the field produced by the expectation value of current. The radiation present can thus be viewed as arising from emission and subsequent reabsorption by matter. As developed here, the numerical predictions of dispersion theory are identical to those of quantum electrodynamics. The physical picture implied by dispersion theory is discussed in the context of semiclassical theories and quantum electrodynamics.

We propose a Wigner transformation of the density matrix and operators of a system with bounded coordinates and discrete momentum spectra (typically, a particle in a box) and prove that all requirements for such a transformation are satisfied. The phase-space mapping adopted here is employed to compute the quasiprobability distributions associated with the pure states of a quantum rotator and the image of the angular momentum operator. The mapping of the dynamics of these objects, both in the reversible and irreversible frame, is constructed as well, and the conditions for the existence of a classical limit in the form of a Fokker-Planck equation of motion are investigated.

The method of intertwining is used to construct transformations between one-dimensional electric potentials or one-dimensional external scalar fields for which the Dirac equation is exactly solvable. The transformations are analogous to the Darboux transformations between Schrödinger potentials. It is shown that a class of exactly solvable Dirac potentials corresponds to soliton solutions of the modified Korteweg–deVries (MKdV) equation, just as certain Schrödinger potentials are solitons of the Korteweg–deVries equation. It is also shown that the intertwining transformations are related to Bäcklund transformations for MKdV. The structure of the intertwining relations is shown to be described by an N=4 superalgebra, generalizing supersymmetric quantum mechanics to the Dirac case.

Beginning with a previously developed theory of the fusion reaction in the dt${\mathrm{\mu }}^{\mathrm{-}}$ system [Belyaev, Révai, and Zubarev, Phys. Lett. B 219, 157 (1989)] we have derived a calculation scheme of the muon-sticking probability in μ-catalyzed fusion that generalizes the commonly adopted sudden approximation. We have found a large nuclear resonance effect on the sticking coefficient. Our calculations disagree with the values extracted from the experiments by Breunlich et al. [Phys. Rev. Lett. 58, 329 (1987)] while they seem to confirm those of Jones et al. [Phys. Rev. Lett. 58, 1407 (1987)].

For a nonrelativistic hydrogenic atom, the dimension dependence of the energy levels is nonsingular except for a second-order pole at ${\mathit{D}}^{\mathrm{*}}$=3-2n, where n is the principal quantum number. For the relativistic Klein-Gordon and Dirac equations, the dimension dependence has a much more complicated singularity structure, involving branch points. For all eigenstates there are branch points at ${\mathit{D}}^{\mathrm{°}}$±2Zα, where Z is the nuclear charge, α is the fine-structure constant, and ${\mathit{D}}^{\mathrm{°}}$ is independent of n but varies linearly with orbital angular momentum. For most states there is in addition a pair of branch points near ${\mathit{D}}^{\mathrm{*}}$ but slightly off the real axis. The customary perturbation expansion in terms of Zα gives qualitatively incorrect dimension dependence; it predicts only poles located on the real axis at ${\mathit{D}}^{\mathrm{*}}$ and ${\mathit{D}}^{\mathrm{°}}$, no matter how high the order of the expansion. The dimensional singularities result from the behavior at r=0. The qualitatively incorrect results occur because the perturbing potential, proportional to ${\mathrm{\alpha }}^2$/${\mathit{r}}^2$, overwhelms the unperturbed 1/r potential at small r. Because of the complexity of the dimensional singularity structure, the popular ‘‘shifted expansion’’ method for summing the 1/D expansion does not work well for these equations. We demonstrate a general method for identifying the dimensional singularities that leads to an exact summation of the 1/D expansion for all eigenstates of both the Klein-Gordon and the Dirac equations for a particle in a Coulomb potential.

The lifetime of the 5d6p ${}_{}{}^3{}_{}{}^{}$F${\mathrm{°}}_4$ level of singly ionized lanthanum has been studied using the ‘‘extended average level’’ version of the multiconfiguration Dirac-Fock method. In order to account for intravalence correlation, the relativistic counterparts of the 5d6p, 4f6s, and 4f5d configurations have been used to describe the upper state, whereas those corresponding to the 5${\mathit{d}}^2$, 5d6s, 4f6p, and 4${\mathit{f}}^2$ configurations are allowed to mix in forming the lower states. The valence-core-electron correlation is included in the computation in an approximate way by means of the core-polarization model. The resulting lifetime of the 5d6p ${}_{}{}^3{}_{}{}^{}$F${\mathrm{°}}_4$ level of La is 4.6 ns and is shorter than the value (6.0±1.0 ns) measured in a beam-foil experiment.

We report a modified time-dependent local-density-approximation (TDLDA) calculation of the linear polarizability of rare-gas atoms. The modification we use takes the self-energy into account by introducing a scissors operator; we simply increase the energy differences of the occupied and unoccupied orbitals from the LDA calculation by a constant. The energy shift is (1) estimated with a single oscillator model and (2) determined such that the modified TDLDA with the scissors operator gives the experimental value of the static linear polarizability. The ratio of the energy shift to the lowest LDA energy difference between occupied and unoccupied orbitals for each atom is calculated. These ratios are found to be comparable to the corresponding ratios of the energy shift to the energy gap in the scissors operator in a solid. The modified TDLDA calculation with the scissors operator agrees better with the experimental results, for the frequency dependence of the linear polarizability, than the TDLDA calculation. We apply the Schmidt-Ruedenberg even-tempered Gaussian basis in our calculation and find that the energy-optimized basis set gives a rather poor convergence rate for the linear polarizability. However, a good convergence rate can easily be obtained by adding a few diffuse basis functions to an energy-optimized basis set.