The charge distribution around an atom in a strongly coupled plasma is calculated for equilibrium states constrained to produce a specified electric field at the atom. It is shown that recently developed methods for electric microfield distributions can be applied directly to calculation of the charge distribution functions as well. Two such methods are considered: effective-field independent-particle models and integral equations with complex potential.

Static and dynamic properties of the fractal sets generated by free and k-tolerant walks are analyzed in detail. A rather complete picture is obtained for the set of the intersections of free random walks, using correlation functions like the probability of visiting one or more sites m times. Monte Carlo enumerations, jointly with rather sophisticated numerical analysis, are used to determine the fractal dimension of the set of the self-intersections of k-tolerant walks. The results are used to throw new light on the Flory argument for polymer chains with excluded-volume effects; the universal behavior of k-tolerant walks is explained in a coarse-grained reinterpretation of the Flory approximation. Diffusion on the same class of walks allows us to discuss also their universality with respect to dynamical properties. In particular, a spectral dimension equal to (4/3 is obtained for the free random walk in d=2 dimensions.

Each of the moments of the current distribution in self-similar networks scales with a different exponent. The Legendre transform of these exponents as a function of the order of the moment is called f(α). In general f(α) has a fixed convexity, has a maximum value equal to the usual fractal dimension, is continuous, is positive, and has a finite support ${\alpha }_{\min <\mathrm{\alpha }<{\alpha }_{\max }}$. Also, it usually characterizes the asymptotic form of the current distribution. Here, explicit examples of physically acceptable exceptions to the behavior of f(α) are exhibited. In the first example, the moments near the zeroth one do not converge uniformly in the large-size limit, leading to an f(α) which has an apparent maximum at a finite value of α while the true maximum is at ${\alpha }_{\max =\mathrm{\infty }}$. In the second example, it is shown that f(α) can take negative values in domains which are relevant for a full characterization of the current distribution. Disorder seems essential to obtain the latter behavior which for these systems compromises the interpretation of f(α) as a continuous set of fractal dimensions.

A phenomenological approach to dissipative tunneling, originally put forth by Pollak [Phys. Rev. A 33, 4244 (1986)], is discussed and contrasted with the bounce formalism. This phenomenological approach is based on the WKB theory for parabolic barrier tunneling. It is quite simple and readily evaluated. We study the results for the leading exponential dissipative decay rate in metastable potentials and contrast them with previous instanton-type (bounce-technique) calculations. In doing so, we compare the zero-temperature decay rate in various metastable potentials, different dissipation mechanisms, and also consider the rate enhancement at very low temperatures. One finds between the two methods unexpected good agreement at weak to moderate dissipation strength; the accuracy decreases with increasing dissipation strength and increasing deviation from a harmonic barrier shape.

The critical heat capacity associated with the nematic (N) to smectic-A (SmA) phase transition has been studied in mixtures of nonpolar heptyloxypentylphenylthiolbenzoate (7¯S5) and polar octyloxycyanobiphenyl (8OCB). In this system, which exhibits both an N-SmA-SmC multicritical point and an N-SmA tricritical point, the N-SmA transition temperature $T_{\mathrm{NA}}$ increases very rapidly as the 8OCB mole fraction X is increased. Data were obtained for a sample near the tricritical composition, for two compositions where the N-SmA transition is second order, and for three compositions exhibiting weakly-first-order transitions. Because of the large values of ${\mathrm{dT}}_{\mathrm{NA}}$/dX, Fisher renormalization was observed. The finite cusp in $C_p$ near the tricritical point yields the renormalized critical exponent ${\alpha }_R$=-0.93±0.17. Since ${\alpha }_R$=-α/(1-α), this corresponds to α=0.48±0.05, in good agreement with the value 0.5 expected at a Gaussian tricritical point.

We have performed high-resolution x-ray scattering studies of the binary liquid-crystal system of octyloxycyanobiphenyl and heptyloxypentylphenylthiolbenzoate (80CB+7¯S5) near the nematic–smectic-A–smectic-C (NAC) multicritical point. We find that the phase diagram and smectic-order fluctuations are well described by a Lifshitz-point model. Above the nematic–smectic-C(N-SmC) phase boundary, we find a line along which the fluctuations change from being SmA-like to SmC-like; this is signaled by the vanishing of the transverse quadratic term in the expression for the x-ray scattering intensity; that is, the transverse fluctuations scale like $q_{\perp }^{\mathrm{-}4}$. The geometry of this Lifshitz line appears to mirror that of the SmA-SmC boundary. A much more extended SmC fluctuation region is observed for lower concentrations of 80CB. Thus the N-SmC pretransitional area is divided into two regions: a pure N-SmC region and a multicritical region. The tilt angle exhibits a first-order transition at the N-SmC boundary. Along the SmA-SmC phase boundary, the tilt is well described either by a power law with an average exponent β=0.43±0.03 or by mean-field theory including a sixth-order correction. No crossover to critical or tricritical behavior is observed as the NAC point is approached. Along the N-SmA phase boundary, we observe second-order N-SmA transitions with average values of the exponents in this region of ${\nu }_{?}$=0.90, ${\nu }_{\perp }$=0.75, and γ=1.55 for the parallel and perpendicular correlation lengths and susceptibility, respectively. Very near the NAC concentration, we observe multicritical behavior, with the above exponents renormalized by the crossover exponent of the N-SmA phase boundary.

The problem for random packing or filling has been treated in many fields. In this paper we form random sequential packing patterns, filling metallic squares with integer length a on insulator substrates divided into square unit cells. We investigate the percolational and fractal property of the packing patterns, and clarify that the maximum critical percolation length $a_c$ (=3 units length) of the packed squares is presented for the insulator-to-metal transition to take place on the random sequential packing textures. When a>$a_c$, no insulator-to-metal transition occurs even at the saturation coverage where no more squares can be filled without any overlap. However even in such patterns with a>$a_c$, the large percolation clusters possess fractal properties, and the fractal dimensions equal 1.94.

The optical-field-induced Fréedericksz transition for a twist deformation by a normally incident laser beam in a planar-aligned nematic liquid crystal is studied. The Euler equation for the molecular director and the equations describing the evolution of the beam polarization in the birefringent medium are solved simultaneously in the small-perturbation limit. The stability of the undistorted state is investigated. An alternate series of stable and unstable bifurcations is found. This phenomenon has no analog in the Fréedericksz transition induced by dc electric and magnetic external fields.

It is shown that statistical-mechanical properties as well as irreversible phenomena of stochastic systems, which consist of infinitely many coupled nonlinear oscillators and are capable of exhibiting phase transitions of mean-field type, can be successfully explored on the basis of nonlinear Fokker-Planck equations, which are essentially nonlinear in unknown distribution functions. Results of two kinds of approaches to the study of their dynamical behavior are presented. Firstly, a problem of asymptotic approaches to stationary states of the infinite systems is treated. A method of Lyapunov functional is employed to conduct a global as well as a local stability analysis of the systems. By constructing an H functional for the nonlinear Fokker-Planck equation, an H theorem is proved, ensuring that the Helmholtz free energy for a nonequilibrium state of the system decreases monotonically until a stationary state is approached. Calculations of the second-order variation of the H functional around a stationary state yield a stability criterion for bifurcating solutions of the nonlinear Fokker-Planck equation, in terms of an inequality involving the second moment of the stationary distribution function. Secondly, the behavior of critical dynamics is studied within the framework of linear-response theory. Generalized dynamical susceptibilities are calculated rigorously from linear responses of the order parameter to externally driven fields by linearizing the nonlinear Fokker-Planck equation. Correlation functions, together with spectra of the fluctuations of the order parameter of the system, are also obtained by use of the fluctuation-dissipation theorem for stochastic systems. A critical slowing down is shown to occur in the form of the divergence of relaxation time for the fluctuations, in accordance with the divergence of the static susceptibility, as a phase transition point is approached.

The influence of noise and resonant perturbation on a dynamical system in the vicinity of a period-doubling bifurcation is investigated. It is found that the qualitative dynamics can be revealed by simple considerations of the Poincaré map. These considerations lead to a shift of the bifurcation point which is proportional to the square of the amplitude of the perturbation. The results of this investigation are in agreement with numerical calculations for the microwave-driven Josephson junction.

The trajectory scaling function for period-doubling bifurcations in four-dimensional symplectic maps is developed. It is a local basis expansion of the nearest-neighbor vectors of the (n+1)-times-bifurcated orbit in terms of the nth. It provides a complete description of the orbits on the way to infinite period doubling. As an application, the scaling function is used to predict the spectrum of singularities.

We derive the exact Mayer series for the pressure, density, and the equation of state of a hard-sphere fluid in the limit of infinite space dimensions D. The Mayer series can be analytically continued into the full (cut) activity plane and there is no sign of a phase transition. We also treat the quantum-mechanical system. For D=∞ the fluid behaves like an ideal Bose gas and undergoes a Bose-Einstein condensation.

Light-scattering experiments have been carried out on an entanglement gel with a binary-liquid mixture as solvent. The onset temperature for critical opalescence has a composition dependence which is similar to the coexistence curve of the free-liquid mixture. This system resembles previously reported work on the cross-linked gel polyacrylamide in two ways: (1) As temperature is lowered toward the critical temperature of the free-liquid mixture, the binary-fluid gel exhibits a strong and increasing light scattering over a broad temperature region of several kelvins, and (2) no appreciable temporal fluctuations are observed throughout this temperature region. Two added features are observed in the present, entanglement-gel measurements: (a) Gel samples with solvent composition both near and off the critical composition of the free-liquid mixture exhibit similar light-scattering behavior, and (b) a Lorentzian-squared fit to the light-scattering angular distributions yields a characteristic wave number which does not change with temperature and an amplitude which shows a very strong dependence on the temperature.

We have applied the Wigner–distribution-function formalism for the determination of the quantum corrections, which appear in the ħ series expansion of the various ‘‘almost classical’’ properties of a many-body system. We have calculated the various averages which appear in the quantum corrections by means of molecular-dynamics computer simulation, up to the order ${ħ}^6$ for the case of Boltzmann particles interacting via a Lennard-Jones potential. Here we report the results of the calculation for the potential and kinetic energies, for the pressure, for the free energy, and for the radial distribution function g(r) at nine different thermodynamic points. The application to the case of He, Ne, Ar, ${\mathrm{H}}_2$, and ${\mathrm{D}}_2$ are given whenever the ħ series expansion can be considered convergent. The advantages and disadvantages of our method are also discussed.

We apply the technique of simple cell mapping to the problem of the rf-driven Josephson junction, and show that this technique is a computation-efficient method of exploring attractors and basins in this system. We show attractors, basins, and Poincaré maps of a previously reported interior crisis, and we also explore the phase plane of a junction with extreme underdamping—an impractical problem by any other technique.

A modification of Yuen’s contractive-state scheme for monitoring free-mass positions is proposed. It involves repeated quantum-nondemolition position measurements and state manipulation following ideas of Lamb, and is reminiscent of the spin-echo technique in nuclear magnetic resonance.

The relation of a previous paper on the parametric amplification of a quantum oscillator to squeezed states is described. In particular, we show that in general the amplification factor is also the ‘‘squeezing factor’’ of the final state.

An advanced accelerator is proposed. The counterstreaming-electron-beam wake-field accelerator replaces the stationary background plasma of the plasma wake-field accelerator by a magnetized electron beam (relativistic factor ${\gamma }_d$), drifting antiparallel to the driving electron beam and driven particles. Both the transformer ratio and the plasma wavelength are increased by a factor of f∼2${\gamma }_d$, thus dramatically enhancing the energy gain of the driven particles per acceleration stage. Furthermore, the particle-trapping threshold is greatly reduced so that proton acceleration may be possible.

Computations are reported in which the hexagonal lattice gas is used to simulate two-dimensional Navier-Stokes shear flows. Limitations associated with noise in the initial loading and compressible effects associated with a velocity-dependent equation of state arise and interact with each other. A relatively narrow window in density and flow speed exhibits physical behavior.

Little’s synchronous model for a neural network is studied in the regime when an infinite number of patterns is to be stored. We show that its retrieval capacity may become much larger than in Hopfield’s model, revealing a greater robustness of synchronous update to noise. The phase diagram, including a parameter controlling the occurrence of cycles, exhibits paramagnetic, ferromagnetic, and spin-glass phases together with a line of tricritical points.