Using an analytic method of solution developed by Varma and Rao [Phys. Lett. 79A, 311 (1980); J. Plasma Phys. 27, 95 (1982)], we obtain exact stationary solutions of a coupled set of time-dependent nonlinear equations [namely, the coupled Schrödinger–Korteweg–de Vries (Boussinesq) system] appropriate for electromagnetic waves propagating along an external magnetic field with a group velocity near the ion-acoustic velocity. The high-frequency field envelope has an antisymmetric structure whereas the low-frequency density perturbation is symmetric. For a given magnetic field strength, left-circularly polarized waves have larger amplitudes than the right-circularly polarized waves; a similar dependence is found also for the associated density perturbations. A set of integral invariants for the time-dependent equations is obtained and explicitly evaluated for the exact solutions. A detailed comparison of the present results with those obtained earlier for the exact stationary equations is carried out. Several improvements as well as extensions of the present theory have been indicated.

The Onsager-Thomas-Fermi diatomic confined molecule for the one-component plasma (OCP) is composed of a pair of point ions, with separation r and a uniform neutralizing charge density of electrons. Its shape is determined by the (‘‘isolation’’) condition that the total electrostatic potential and field vanish outside its boundary. These uniquely defined objects are obtained variationally from the high-density (ρ→∞) solution of the hypernetted-chain (HNC) equation for an OCP in which certain ion pairs are constrained to have fixed separation r. The HNC variational problem is mapped on the Onsager ‘‘charge-smearing’’ optimization for obtaining the best lower bound for the interaction potential energy of the system. We outline the derivation of these ‘‘molecules’’ as natural generalizations of the ion-sphere Thomas-Fermi (TF) ‘‘atom.’’ Their shapes and self-energies are determined numerically and are compared with various approximations. The self-energies of these diatomic molecules provide excellent estimates of the short-range part of the OCP pair correlations and are rather insensitive to the optimization. Our results represent the ρ→∞ or T→∞ solution of the general confined-molecule TF equation, which is also solved at T=0 for finite but still high densities. Electron-screening contributions to the confined-molecule TF energies are interpreted in terms of the solution of the HNC integral equation for a Yukawa potential.

The stochastic dynamics of randomly asymmetric fully connected Ising systems is studied. We solve analytically the particularly simple case of fully asymmetric systems. We calculate the relaxation time of the autocorrelation function and show that the system remains paramagnetic even at zero temperature (T=0). The ferromagnetic phase is only slightly affected by the asymmetry, and the paramagnetic-to-ferromagnetic phase transition is characterized by a critical slowing down similar to second-order transition in symmetric (fully connected) systems. Monte Carlo simulations of a fully connected Ising system with random asymmetric interactions, both at finite and zero temperature, are presented. For finite T the autocorrelation function decays completely to zero for all strengths of the asymmetry. The T=0 behavior is more complex. In the fully asymmetric case the system is ergodic, with decaying autocorrelations, in agreement with the theoretical predictions. In the partially asymmetric case all flows terminate at fixed points (i.e., states which are stable to single spin flips). However, the typical time that it takes to converge to a fixed point grows exponentially with the size of the system. This convergence time varies from sample to sample and has a log-normal distribution in large systems. On time scales which are smaller than the convergence time, the system behaves ‘‘ergodically,’’ and the autocorrelation function decays to zero, much like the finite-temperature case.

The complete vibrational frequency spectrum of several DNA double-helical oligomers is calculated using established pair potentials. Various cutoff values are used for the range of the Coulomb interactions. At very low frequency the integrated density of states shows a noninteger exponent with values ranging from 0.75 to 1.55, depending on the cutoff value for the Coulomb interactions. We conclude that the cumulative densities of states in those molecules depend more on competing interactions than on various proposed universal laws.

A model of diffusive equilibrium density fluctuations in a grand-canonical ensemble is constructed for systems of finite size. The particle number autocorrelation is developed from a Langevin-type bounded-diffusion equation. Both probe and sample geometries affect its spectrum, which factors into two terms representing the particle creation rate and diffusion according to a multidimensional Carson’s theorem. The spatial decay of the kernel in the spectrum’s integral equation is measured by a frequency-dependent correlation length that depends on particle lifetime, diffusivity, and probe resolution. The kernel and its transform, the mutual coherence function, collapse to the Ornstein-Zernike spatial distribution but with the new result that the classical correlation length is given by a ratio of diffusive and thermodynamic variables. For the limiting case of an unbounded system with infinite particle lifetime, Voss and Clarke’s spatially correlated spectrum is rederived.

However, for this ensemble a finite particle lifetime is a necessary equilibrium condition. Little’s theorem is generalized when particle interactions are included. Noise-power integrals converge in all cases. Frequency exponents characterize the spectra and, when a small region is probed in a quasi-two-dimensional system, broadband 1/f noise occurs. A Lorentzian spectrum results in the limit of no diffusion. A lower length limit introduced to avoid the breakdown of the diffusion approximation at small time and space intervals can in some cases be identified with probe resolution and is measurable when a certain crossover in frequency exponents is identified. The analysis is then applied to fluctuations in the electron current, thermal field emitted from a single-crystal tungsten cathode. These are coupled to self-diffusion of surface defect adatoms on the cathode by the Fowler-Nordheim equation. Other frequency crossovers yield surface diffusivities and their activation energies, which for comparable W(h k l) planes are consistent with field-ion microscopy measurements. The defect vacancy activation energy is estimated from the temperature dependence of the adatom creation rate and is similar to that obtained from emitter surface-tension measurements. For the projection optics of field emission systems spatial resolution is mapped to the Gaussian source diameter $d_g$. Using this new measurement method $d_g$≃20 Å is obtained for 1000 K thermal-field emission from tungsten.

Dynamical states and bifurcations of a thermal lens are studied with use of spectral analysis. The following dynamical states are observed: steady, periodic, quasiperiodic with two fundamental frequencies, and subharmonic states. Hysteresis is observed in the transition between periodic and quasiperiodic oscillations. Although chaos is not observed in the present work, thermal-lens oscillations can also lead to chaos as previously published. The control parameters are the laser power P and a distance d. The boundaries of the different dynamical states are given in the plane (P,d). Properties of the different dynamical states and of the transitions between states are studied.

We analyze the minimal conditions required to build up a coherent and neutral-like description of critical phenomena in strongly coupled binary mixtures of pointlike positive charges. One is thus led to bridge the gap between the microscopic approach dealing with the divergence of the ionic structure factors $S_{\alpha \beta }$(k) in the k→0 limit and the thermodynamic one deduced as usual from the Gibbs free-energy function. We emphasize the fundamental role played by the electronic polarization. Namely, modeling the plasma in the so-called polarized binary ionic mixture which accounts for the electronic density fluctuations through a static dielectronic function ε(k), we show that the ionic mixture may be properly described as a mixture of ‘‘pseudoatom’’ if ε(k) fulfills the compressibility sum rule while the weak electron-ion coupling hypothesis is assumed to be valid. Conversely, the binary ionic mixture model, with no electronic polarization at all, appears to be inappropriate to the microscopic approach, as a consequence of the rigid character of the electron background.

The microscopic analysis detailed in the preceding paper (I) is pursued here with a thorough presentation of the correlation functions taken in the small-k limit. Demixing is investigated numerically through two different models differing by the stage at which the electron dielectric function is introduced into the formalism.

A new principle of statistical estimation is formulated here. It stresses the maximum utilization of all the information one has in physical and mathematical statistical estimation problems. The method of incorporation of additional information used is via the invariants of the problem at hand. After enunciation, the new principle is illustrated by means of a conservative dynamical system. Next, concrete applications are reviewed, including curve-fitting problems. Extension to systems with broken symmetries or dissipative forces is accomplished through the inclusion of adiabatic invariants. In addition, the construction of confidence intervals for the estimates and a proof of their correctness (when the information is minimally complete) is provided. Finally, the fundamental postulate of statistical mechanics is derived from the new principle of statistical estimation.

The optimal control of the path to a specified final state of a quantum-mechanical system is investigated. The problem is formulated as a minimization problem over appropriate function spaces, and the well-posedness of this problem is is established by proving the existence of an optimal solution. A Lagrange-multiplier technique is used to reduce the problem to an equivalent optimization problem and to derive necessary conditions for a minimum. These necessary conditions form the basis for a gradient iterative procedure to search for a minimum. A numerical scheme based on finite differences is used to reduce the infinite-dimensional minimization problem to an approximate finite-dimensional problem. Numerical examples are provided for final-state control of a diatomic molecule represented by a Morse potential. Within the context of this optimal control formulation, numerical results are given for the optimal pulsing strategy to demonstrate the feasibility of wave-packet control and finally to achieve a specified dissociative wave packet at a given time. The optimal external optical fields generally have a high degree of structure, including an early time period of wave-packet phase adjustment followed by a period of extensive energy deposition to achieve the imposed objective. Constraints on the form of the molecular dipole (e.g., a linear dipole) are shown to limit the accessibility (i.e., controllability) of certain types of molecular wave-packet objectives. The nontrivial structure of the optimal pulse strategies emphasizes the ultimate usefulness of an optimal-control approach to the steering of quantum systems to desired objectives.

The growth of a droplet pattern condensing on a surface (e.g., breath figures) is analyzed for the case of arbitrary dimensionality. The growth of a droplet occurs through a two-step process: (i) continuous growth by condensation on its surface and/or on the substrate and (ii) coalescence with neighboring droplets. As long as the one-droplet growth remains scale invariant, the growth of the entire pattern is shown to be self-similar in time and very general growth laws can be deduced, whose exponents are functions only of the dimensionality of the space of the droplets, and of the condensing substrate. In particular, for the case of three-dimensional droplets condensing on a plane substrate (breath figures), the growth exponent of a single droplet should be (1/3, whereas the exponent corresponding to a mean droplet, averaged over the pattern, should be unity. Comparison with experiment is performed and possible deviations from the predictions are considered.

The number of quasibound or rotationally predissociating levels of diatomic molecules is investigated using a long-range approximation of the difference between the Jeffreys-Wentzel-Kramers-Brillouin estimates of the vibrational quantum numbers at the maximum of the rotational barrier and at the dissociation limit. It is found that for a fixed J the expected number of quasibound levels is approximately J/20, essentially independent of the magnitude and form of the potential and independent of the mass of the nuclei.

Angular distributions of continuum radiation emitted during proton–aluminum-atom collisions are investigated. Atomic bremsstrahlung (AB) including retardation effects is calculated and compared with available experimental data. Angular distributions are found to be asymmetric with the maximum shifted towards angles smaller than 90°. A good agreement with the experiments is found where AB is dominant over the secondary-electron bremsstrahlung, i.e., for photon energies larger than $T_m$=2$v^2$, where v is the ion velocity.

Photoelectric cross sections for low-energy photons in the energy range of 5.9 to 20.16 keV in beryllium, carbon, aluminum, magnesium, silicon, copper, silver, and lead have been determined experimentally through photon-transmission measurements performed under narrow-beam counting geometry with Si (Li) as a photon detector. The photoelectric-cross-section values reported in this work are found to be in agreement with the values computed theoretically by E. Storm and H. I. Israel [Nucl. Data Tables A 7, 565 (1970)].

We report triply differential cross sections for electron-impact ionization of atomic hydrogen for near-symmetric geometry at incident energies of 250 and 100 eV. The calculation is based on the Glauber approximation (GA). The effect of the post-collision interaction (PCI) is incorporated in the GA using a classical method. The angular distributions of the ejected electrons predicted by the present method are in reasonably good agreement with experiment. The inclusion of the PCI improves the results considerably.

Transition energies for x-ray hypersatellite lines (K${\alpha }_2^h$) and two-electron–one-photon lines (Kα-Kα) have been calculated for low-Z atoms using a simple variational method with a two-electron correlated wave function. The method gives real insight into the structure of energies of the initial and final states. The results are very encouraging.

The results obtained by Sharma and Roversi on the dynamics of a coherently excited four-level atom are discussed and explained.

The relationship between a recently developed kinetic theory and a Green’s-function approach with respect to the electron shift and broadening of spectral lines is investigated. With the use of a set of approximations common to line-shape theory, it is shown that the two different theoretical approaches lead to identical expressions. The comparison is restricted to neutral radiators.

Extensive dynamical light-scattering experiments have been performed on the critical ternary system water, benzene, and ethanol close to its 25 °C plait point. The experimental results show the theoretically expected renormalization of the critical exponents. Furthermore, the critical slowing down of concentration fluctuations is very well accounted for by the Kawasaki mode-coupling theory including background effects.

We show that solitons and kinks that obey the nonlinear Schrödinger equation and are subject to an external force, constant or not, do travel along a classical trajectory having the same shape as without the external field.