We use an improvement of a three-dimensional model [Phys. Rev. A 27, 2321 (1983)], taking space charge into account for ions confined in a quadrupole rf trap. This model allows us to calculate the spatial and energy probability densities of strongly confined ions in the presence of a light buffer gas and shows the evolution of these properties as the total number $n$ of ions increases. The ions are ${\mathrm{Ce}}^{+}$ in the presence of dilute helium. For the chosen working point, the distributions remain Gaussian when $n$ does not exceed (2-3) × ${10}^5$ ions at room temperature. The influence of the temperature on the importance of space-charge phenomenon is also studied.

The method of harmonic balance is used to obtain analytic results for the differential equation describing a current-biased Josephson junction with self-capacitance that is shunted by a resistor with substantial self-inductance. This system is known to exhibit period-doubling cascades, chaos, and other exotic nonlinear phenomena. After an accurate representation of the basic voltage oscillation is determined for high-bias currents, the value of bias current is computed for which this solution loses stability to a period-doubled mode. The predictions agree to remarkable accuracy with results obtained from both analog simulations and digital integration of the circuit equation, typically 5% for moderate values of inductance. Moreover, the method of calculation provides a systematic scheme for achieving increasing accuracy.

Momentum-analyzed beams of 20 and $17.326 \frac{\mathrm{GeV}}{c}$ electrons with average currents of 4.23 and 4.55, and 9.48, 9.57, 14.4, and 15.66 μA, respectively, are predicted by special relativity to have average powers of 84.5 and 91, and 164.3, 165.8, 249.5, and 271.3 kW, respectively. This prediction is checked to 30% in a calorimetric experiment using the temperature rise in the cooling water of a high-energy beam dump at the Stanford Linear Accelerator Center. To our knowledge, this is the first macroscopic test specifically carried out to test this aspect of special relativity at these particle energies and power levels, although an earlier sequence of tests using copper as the heat absorber have been performed at this laboratory at lower power levels, and confirms the theory to higher accuracy.

Diffusion of a particle on a one-dimensional disordered lattice is studied using the renormalization-group (RG) procedure of Goncalves da Silva and Koiller [Solid State Commun. 40, 215 (1981)]. The RG equations are derived and their physical content is discussed. Several examples are studied using the RG equations and a disorder-averaging procedure that permits stepwise averaging of the RG equations. Values of the diffusion constant so calculated, while qualitatively correct, are in poor agreement with the known correct answer. The RG equations are shown to be derivable from a dedecoration carried out on a replica-trick description of the diffusion process. Employing the relationship of the RG equations to dedecoration, a stepwise disorder-averaging procedure is constructed that yields values of the diffusion constant in excellent agreement with expectations. The relationships of the RG equations to the renormalization-group treatment of Machta [Phys. Rev. B 24, 5260 (1981)] and to the logistic equation are discussed.

Nonlinear-response theory to quadratic order in the external electric field is used to derive correlation-function expressions for the hydrodynamic disturbances caused by the absorption of light in linear spectroscopy. For relatively low-frequency sound, this treatment is shown to give the phenomenological expression for the pressure generated by adiabatic expansion of the solvent. In addition, two new terms are obtained. These represent the direct coupling between the dynamics of the absorbers and the local microscopic stress. One of these terms has a dependence on the polarization of the incident light which is totally absent in the phenomenological theory. A photoacoustic experiment is suggested which can measure this new effect.

The hard-spheres fluid near a wall is investigated using the superposition approximation in a virial approach. Three new virial coefficients (fourth, fifth, and sixth) of the density profile are given. These new coefficients are used to obtain the corresponding new virial coefficients for the adsorption and for the surface tension. In this case, statistical and thermodynamic equations are used. The results are compared with full numerical calculations in the same approximation and using the Percus-Yevick closure.

A controversy which has appeared recently in the literature surrounding the topic of this paper has so far left open the question of whether the Boltzmann equation is invariant under rotation of the reference frame, and speculations regarding exotic consequences of the Coriolis acceleration have yielded physically paradoxical results. In this paper it is shown that by consistently using generalized canonical dynamical variables appropriate to a rotating reference frame, the exotic paradoxes dissolve, and a proof emerges that the physical consequences of the Boltzmann equation are invariant with respect to the rotation of the frame of reference.

We calculate the energy loss of charged particles in nondegenerate plasmas using classical and quantum-mechanical approximations. First we consider classical binary collisions between the test particle and the particles in the plasma, and obtain the energy transferred as a function of the relative velocity. This is integrated over the thermal distribution of plasma-particle velocities using simple analytical approximations. Then we use the quantum-mechanical analysis of the scattering of partial waves to find the transport cross section for a screened potential, and introduce analytical approximations to calculate the phase shifts. The thermal average is also calculated analytically. The study yields simple expressions for the energy loss in terms of the velocity and charge of the particle and of the density and temperature of the plasma. In particular, we retrieve various results of previous authors, which apply as limiting cases in the classical or quantum-mechanical regimes. The transition between these cases is described by analytical expressions of excellent accuracy. The calculation is finally compared with experimental results from laboratory plasmas in the classical domain.

The dynamics of the first-order phase transition in systems with $p$-fold degeneracy ($p\ge 2$) is discussed. A scaling analysis of a phenomenological kinetic equation is discussed to obtain various prototypes of droplet growth rates from a unified viewpoint. A process of repetitious switching of the growth mechanisms is discussed relying on the dynamic-scaling assumption. The effect of this process gives the growth rate of droplet radius $R \propto t^{a^{*}}$ with $a^{*}$ being a weighted average of the exponents of elementary processes associated. The crossover from a slow growth rate to large one need not occur, nor does the growth rate need to approach a universal law. The final growth rate may depend on system parameters such as concentration, temperature, degeneracy, and so on. Using a simplified cell model, we calculate the droplet growth rate in the case where $p$ phases have the same average density. Droplet radius $R$ grows by means of a curvature-driven force for $p\le p_c-1\mathrm{}\approx 3^d-1\mathrm{}$, and mainly by means of an entropy (or thermal) force for $p\ge p_c^{\prime }\approx 5^d$, where $d$ is the dimensionality. Here $p_c=p_c^{\prime }=2\mathrm{}$ for $d=1\mathrm{}$ and $p_c=7\mathrm{}$ and $p_c^{\prime }=19\mathrm{}$ for $d=2\mathrm{}$, however. For such a temperature as $T<\mathrm{}{T}_c{e}^{-{\xi }^{-1\mathrm{}}R}$ the entropy force does not apply and an exponentially weak attractive force drives droplet growth instead. Here $\xi$ is the thermal correlation length and $T_c$ the transition temperature. The exponent $a^{*}$ takes constant values both for $p<\mathrm{}{p}_c$ and $p>\mathrm{}{p}_c^{\prime }$. For $p_c\le p\le p_c^{\prime }$, $a^{*}$ monotonically decreases as $p$ increases. These predictions are consistent with recent numerical simulations of Sahni et al. and of Sadiq et al.

In this paper we show that a high-frequency plasma instability can lead to auroral kilometric radiation. In the presence of low-frequency ion-cyclotron turbulence and a high-frequency extraordinary-mode ($X$-mode) test wave, this instability occurs due to a nonlinear force which originates from the resonant interaction between electrons and modulated electric fields. The growth rate of the $X$-mode wave, in the form of auroral kilometric radiation, has been calculated and compared with observations.

The high-frequency elastic behavior of fluid surfaces is studied from first principles. The general dispersion equation for elastic surface waves thus obtained reveals the influence of the surface structure on Rayleigh's surface waves. New types of surface waves are also found. Their existence depends crucially on the presence of nonvanishing surface excess elastic moduli and hence these waves are inaccessible to the macroscopic theory of elasticity. The experimental observation of these elastic surface waves could provide new information about the structure of the liquid surface.

The problem of a particle trapped in a quartic double-well potential in the presence of a mono-chromatic external field is studied. Renormalization-group techniques are used to determine at what external field frequencies and amplitudes barrier penetration can occur for a particle initially trapped at a given energy in one of the potential wells.

Fluid processes at high frequencies associated with fluid inertia, compressibility, and viscoelasticity contribute to the spectra of the random force- and velocity-autocorrelation functions of a Brownian particle immersed in water. In addition, the internal rotational degrees of freedom of the fluid particles also contribute to the structure of the correlation functions in both the high- and low-frequency regimes. As we show here, the relative importance of these various effects for translational and rotational Brownian motion depends on the size of the Brownian particle, and on the fluid parameters.

Stochastic layers and secondary resonances are studied for the double-resonance Hamiltonians of Walker and Ford. A detailed analysis of some numerical results is given.

We present a phenomenological model for the phase transition between the monolayer ($S_{A_1}$) and the bilayer ($S_{A_2}$) phases of smectic liquid crystals. This model contains all relevant symmetries and Goldstone modes. We study the transition using the $\epsilon$ expansion and find it to be in the same universality class as the Ising model to first order in $\epsilon$. In three dimensions, the physical correlation function, however, exhibits nonuniversal power-law behavior leading to a nonuniversal susceptibility exponent $\gamma$.

A method is presented for inverting operators in the coherent-states $R$ representation. The method is equivalent to the solution of an ordinary differential equation. The equation is presented in an explicit general form. Some simple nontrivial examples are illustrated. Applications suggested are calculations of resolvents in phase space and semiclassical expansions.

Transition energies from the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ ground state to the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ excited states in the beryllium isoelectronic sequence are calculated using standard multiconfiguration Dirac-Fock theory. These predictions are then compared to those of the multiconfiguration relativistic random-phase-approximation theory and with experiment.

It is shown that the satisfaction of any two of the four anticorrelation identities recently derived by Ullah is a sufficient condition for the wave function involved to be an exact eigenfunction. Furthermore, a particular linear combination is equivalent to the variance, whose vanishing is in itself a sufficient condition for an exact eigenfunction. Further positive semidefinite expressions, whose vanishing is a necessary and sufficient condition for an exact eigenfunction, are suggested. These and related properties are illustrated by means of two simple examples which exhibit some of the underlying features of applying anticorrelation identities to the optimization of trial functions.

The degenerate perturbative treatment of the hydrogenic Zeeman problem is put on a more rigorous basis and is extended to higher levels belonging to the manifolds of $M=n-\left|m\right|\mathrm{}\le 4$ basis states. The $16n=4$ levels are calculated and the large-$n$ behavior of the basis states is discussed.

Peculiar theoretical results have been reported for reactions in the presence of a low-frequency laser field. These reactions are electron-ion scattering, the $e-2e$ reaction, and photoionization. Each has a Coulomb potential in the initial and/or final state. The theory was carried out with a potential $V_R\mathrm{}\left(r\right)\mathrm{}$ which vanishes for $r>R$ and is discontinuous at $r=R$. In response to suggestions that the peculiarities of the results are due to this discontinuity, we demonstrate that they are in fact independent of the way the potential is screened at large distances.