A self-consistent calculation is done to evaluate relevant ground-state properties of the electron gas in the deformable-jellium model. We get the melting point of the Wigner crystal and the ground-state energy per particle at all densities. The single-particle state function in the Slater determinant is expanded in a basis of periodic functions. This expansion guarantees the existence of a particle density centered on a simple-cubic lattice. The transition to the Wigner crystal is obtained as the value of the Wigner-Seitz parameter at the point where the state function changes from a periodic density to a plane-wave density. Our results for the transition density to the Wigner crystal are close to values obtained using alternative methods. The ground-state energy obtained in this work is compared to recently reported theoretical predictions.

The reaction field theory is used to calculate the frequency shift in the generalized squeezed coherent state. The result for the squeezed vacuum state is a special case.

The nutational regime induced by a stochastic field with phase telegraph noise is experimentally investigated in a two-level system at microwave frequency. Regular oscillations are observed in the average transient response of the system with an effective Rabi frequency whose value depends both on the jump amplitude and on the mean dwell time of the phase noise. Motional-narrowing, weak-damping, and strong-damping regimes are observed on varying the dwell time and the jump amplitude. The experimental results are in fair agreement with theoretical predictions.

It is shown that the generalized (Rényi) entropies K(q) exhibit a singular behavior in case of a map characterizing a chaotic cosmological model (the ‘‘Mixmaster’’ universe). Namely, K(q) is infinity for q<(1/2 and the corresponding spectrum of dynamical scaling indices has only an increasing branch without an upper bound. Numerical simulations have been carried out to demonstrate the analytical results.

We argue that the diffusion-limited aggregation grown with a noise-reduction parameter (B) exhibit three different regimes, according to the relative strength of the fluctuations and lattice-induced anisotropy. A scaling law relating these regimes is proposed. In the intermediate regime the fractal dimension is B dependent. The width of the intermediate regime remains practically constant after a critical value $B_c$ of the noise-reduction parameter, indicating that, however small the fluctuations, lattice anisotropy dominates the process only for scales greater than a screening length.

It is shown that the wave function of a particle passing through a constriction experiences a phase shift that is dependent on the geometrical shape of the boundary. For a separable problem the change in the spatial boundary in one of the coordinates brings about a nonlocal potential in the wave equation for the other coordinate. This feature has been studied by solving the Schrödinger equation in the elliptic cylinder coordinates.

We report a derivation of the frequency-dependent conductivity for high-temperature plasmas that takes into account the collective dynamics as well as the short-range correlations. This treatment rests on the joint solution of the first two members of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy when both are able to change on the same time scale. For arbitrary frequencies this leads to an integral equation for the one-particle distribution function that can be solved by conventional variational or numerical procedures. For frequencies that are higher than the collision frequency, an explicit expression for conductivity is obtained. Effects of the short-range correlations are included by introducing an effective interaction. The high-frequency limit is further examined for an infinite ion mass and numerical results are presented.

The Coulomb interaction between a heavy fast charged particle and an electron bound by a harmonic force has been evaluated accurately up to the second-order term in the Born series. The resulting mean energy transfer is given as a function of impact parameter, projectile velocity, and the resonance frequency of the oscillator. Integration over the impact parameter yields the stopping cross section up to third order in the projectile charge $e_1$ without introduction of an adjustable cutoff radius. Unlike previous treatments, the validity of the evaluation of the stopping cross section within the given physical model is not restricted to the high-speed limit. Numerical results cover the velocity range 0.1≤2${\mathrm{mv}}^2$/ħω≤20. We find a significant $e_1^3$ (or Barkas) correction in the mean energy transfer at all impact parameters. The classical Barkas correction, as given for the harmonic oscillator in the high-speed limit by Ashley, Ritchie, and Brandt [Phys. Rev. B 5, 2393 (1972)], approaches the quantal result for large impact parameters, but the approach is slow in the velocity range covered, and large discrepancies are observed in the range of impact parameters that determine the stopping cross section. Stopping cross sections for protons on atomic hydrogen and helium have been estimated roughly by assigning a single resonance frequency to the target atom. The results cover a velocity range down to somewhat below the stopping maximum where the Barkas correction turns out to be large. This indicates that a properly executed Barkas correction plays an important role in the prediction of the height and the position of the stopping maximum.

A theoretical model describing the effect of orientational constraints in diffusion-controlled enzymatic reactions is developed. It involves a rototranslational diffusion problem with mixed boundary conditions, which is solved in a diffusion-jump approximation. In this approximation the reactant molecules are partitioned in two classes. One class (I) includes the molecules which have their internal rotational angles, with respect to the enzyme binding site, within a given angular region C. All the other molecules belong to the second class (II). The relative population of the two classes changes according to interconversion rates which, in the present theory, is related to the true rotational diffusion coefficients of the reactants. The molecules of class I are adsorbed inside of a small circular region of the enzyme, while the ones belonging to class II are reflected everywhere at the surface. The solution of this problem leads to a set of integral equations from which the flux of adsorbed reactant molecules can be calculated. The influence of different physical parameters (rotational and translational diffusion coefficients, size of the enzyme binding region, range of the orientational region C) on the total flux has been investigated by numerical calculations, and some interesting limiting cases have been examined.

A thermodynamic model for phase transitions of multilamellar liquid crystals composed of phospholipid bilayers in water is developed. By means of a Landau theory of the thermally driven hydrocarbon chain-melting transition of an isolated membrane and a continuum model of the interactions between neutral phospholipid bilayers, the phenomenon of structural phase transitions induced by membrane interactions is described. The phenomenological parameters that appear in the theory may be readily determined by existing experimental techniques; an analysis of available data on several phospholipid systems is used here to estimate these quantities. Semiquantitative agreement is achieved with the experimental temperature-composition phase diagram as well as the variation of the characteristic dimensions of the lamellar crystals with water content. Possible origins of pseudocritical phenomena are suggested on the basis of the unusual topology of the phase diagram. The model highlights the central importance of the water-mediated ‘‘hydration repulsion’’ between membranes in the phase behavior of the lamellar systems.

We incorporate local threshold functions into the dynamics of the Hopfield model. These functions depend on the history of the individual spin (= neuron). They reach a maximal height if the spin remains constant. The resulting one-pattern model has ferromagnetic, paramagnetic, and periodic phases. This model is solved by a master equation and approximated by simplified systems of equations that are substantiated by numerical simulations. When several patterns are included as memories in the model, it exhibits transitions—as well as oscillations—between them. The latter can be excluded by known methods. By introducing threshold functions which affect only spins which remain positive, thus mimicking fatigue of the individual neurons, one can obtain open-ended movement in pattern space. Using couplings which form pointers from one pattern to another, our system leads to self-driven temporal sequences of patterns, resembling the process of associative thinking.

Motivated by recent mean-field theories of the structural glass transition and of the Potts glass model we formulate a scaling and droplet picture of an assumed ideal structural glass transition. The phase transition is a random first-order phase transition where the supercooled-liquid phase is composed of glassy clusters separated by interfaces or domain walls. Because of entropic driving forces the glassy clusters are continually being created and destroyed. As the ideal transition temperature is approached the entropic driving force vanishes and the size of the glassy clusters diverges with an exponent of ν=2/d. All long-time dynamical processes are activated and the Vogel-Fulcher law is obtained for the liquid-state relaxation time.

We study classical and quantum mechanics of a rotor in the presence of two interacting nonlinear resonances. Quasienergy states and quasienergies are computed. The widths of the quasienergy states in the representation of the unperturbed angular-momentum levels are found to be closely associated with the classical dynamics. The widths of many resonant quasienergy states are found to be extended by the quantum-resonance overlap when the perturbation is increased. Spectral repulsion is present in these extended states.

We study the node-avoiding (NALF) and path-avoiding extensions of the Lévy flights in terms of the critical exponents ν and γ and the leading corrections to scaling, using Monte Carlo simulations with enrichment as the main technique. We focus on the upper marginal dimensions of NALF as predicted by the magnetic analogy where the renormalization-group results should be quantitatively exact for NALF if the method is valid at all. Similarly, we also focus on the boundary between the long-range and short-range behavior of NALF above four dimensions where the renormalization results should again be exact. Thus we investigate the self-avoiding Lévy flights on hypercubic lattices from d=2 to 6 dimensions and obtain behavior consistent with logarithmic corrections to scaling in the moments of their end-to-end distance distributions. In addition, the effective Lévy index ${\mu }_{\mathrm{eff}}$ is determined from the logarithmic averages of individual step sizes and compared for the two self-avoiding extensions.

The weight systems of level-zero representations of affine Kac-Moody algebras provide an appropriate kinematical framework for studying structured finite systems with adaptive temporal development. Much of the structure is determined by Lie algebra theory, so it is possible to restrict greatly the connection space and analytic results are possible. The time development of these systems often evolves to cyclic temporal-spatial patterns, depending on the definition of the dynamics. The purpose of this paper is to set up the mathematical formalism for this ‘‘memory in Lie algebras’’ class of models. An illustration is used to show the kinds of complex behavior that occur in simple cases.

We have developed a method of investigating the solute concentration field around a dendrite growing from a supersaturated ammonium chloride solution. It uses the refractive index of the solution as a measure of its concentration. The spatial dependence of refractive index is measured with the aid of an interference microscope. The field distributions obtained in this way indicate a nonlinear relationship between growth velocity and driving force. We propose a model for dendritic growth based on homogeneous nucleation at a temperature below the surface roughening temperature. We show that it is consistent with the measurements and also provides a mechanism of pattern selection.

We show that time distributions of photoelectrons can best be described by a generalized probability-density function which we call the probability-density functional. The probability-density functional gives complete information about the statistical properties of any random-point process, and provides the most natural definitions of the ensemble average and generating functional of a quantity distributed in time. Using this functional, we develop a new approach to photoelectron statistics that systematically relates various joint probability distributions of photoelectrons to one another and to the corresponding generating functionals. We demonstrate that this method can be used to derive previously obtained results and we use it to obtain new results. In particular, the amount of information about the statistical properties of photoelectrons that is contained in a probability distribution can be obtained by comparing the corresponding generating functional with the probability-density functional. Further, we examine time derivatives of the probability distribution for the number of counts and develop new relationships for probability distributions of triggered counting. Finally, we apply our results to obtain an ‘‘inverse’’ relationship between photon bunching (antibunching) and super-Poisson (sub-Poisson) statistics.

When the motion of the surrounding heat bath particles is a slow coordinate, a ‘‘system’’ particle and its bath become dynamically coupled. A nonlinear Langevin (Fokker-Planck) equation is required to describe the stochastic process. In general, the steady-state distribution is not canonical. The rapid-motion effect, in association with the dynamical coupling among multimodes of the system, and the combined contributions from nonlinear and non-Markovian processes, cause a breakdown of the conventional Brownian motion theory. The discussion given in this paper puts previous computer-simulation results on a better theoretical foundation.

By means of functional differentiation we have developed a general theory that allows one to perform the virial expansion of correlation functions and spectra. We have applied our results to the case of interaction-induced spectroscopy, for which the experimental determination of two-body and three-body spectra have been performed in several gaseous systems. We show that, in particular, the three-body experimental spectra are composed of three parts with different temperature behaviors, which allows in principle their discrimination.

The generalized Melnikov function is computed for the squeezed double well and is shown to exhibit simple zeros. The effect on the homoclinic behavior due to the renormalization of the barrier height resulting from zero-point oscillations of the phonon is also studied.