Corrections to the adjustable-parameter exponential (APEX) model recently proposed by Iglesias, Lebowitz, and MacGowan for electric field distributions in a strongly coupled plasma are defined and discussed. The results for a neutral point are compared with those from Monte Carlo calculations for two values of the plasma parameter, and good agreement is obtained.

Attractor structure on the real line is represented as a mass function M(x) defined as the fraction of attractor points to the left of x. For Feigenbaum attractors, M is a devil’s staircase which possesses both orbit and mass scaling features. The attractors ${\mathrm{scrA}}_p$ for maps with a pth-order extremum are discussed in terms of this scaling, which leads to a hierarchy of bounds for the corresponding mass $M_p$. Both ${\mathrm{scrA}}_p$ and $M_p$ transform in a characteristic way under power-law conjugacy; this gives rise to two kinds of global scaling. A further intermediate scaling for the quartic attractor which underlies vector scaling in two-extremum maps is discussed in this context. As p tends to infinity, the capacity dimension D tends to 1 and the information dimension σ to 0. The effects of this trend on the appearance and observability of attractors are discussed.

Nosé has modified Newtonian dynamics so as to reproduce both the canonical and the isothermal-isobaric probability densities in the phase space of an N-body system. He did this by scaling time (with s) and distance (with $V^{1/D}$ in D dimensions) through Lagrangian equations of motion. The dynamical equations describe the evolution of these two scaling variables and their two conjugate momenta $p_s$ and $p_v$. Here we develop a slightly different set of equations, free of time scaling. We find the dynamical steady-state probability density in an extended phase space with variables x, $p_x$, V, ε̇, and ζ, where the x are reduced distances and the two variables ε̇ and ζ act as thermodynamic friction coefficients. We find that these friction coefficients have Gaussian distributions. From the distributions the extent of small-system non-Newtonian behavior can be estimated. We illustrate the dynamical equations by considering their application to the simplest possible case, a one-dimensional classical harmonic oscillator.

We evaluate the low-frequency component electric microfield distribution at a charged point, i.e., the field distribution due to ions, possibly of different species, which interact through an electron-screened potential. The method employed is an adaptation of the adjustable-parameter exponential (APEX) approximation previously developed for the high-frequency component and involves a noninteracting-quasiparticle representation of the electron-screened ions designed to yield the correct second moment of the microfield distribution. The APEX results are compared to Monte Carlo simulations, and we find good agreement.

A new treatment is applied to the Firpo-Legré-Bois-Baret model for the liquid-expanded–liquid-condensed phase transition of amphiphilic monolayers at the air-water interface. Stresses of mean-field type are introduced in the Migdal-Kadanoff decimation procedure. The processing of the new recursion relations is the same as in a previous paper [J. P. Legré et al., Phys. Rev. A 30, 2720 (1984)] and gives computed isotherms in the surface pressure-molecular area plane, with a compressibility jump like certain experimental ones. The results verify part of our previous assumptions.

We discuss the phase-space representation of the Bloch equation and present analytic expressions for two generalized classes of distribution functions. Series solutions to order of ${ħ}^2$ are given. We conclude that the Wigner quantum corrections are the simplest among the two general classes of distribution functions.

We construct a theory of velocity selection and tip stability for dendritic growth in the local evolution model. We show that the growth rate of dendritic patterns is determined by a nonlinear solvability condition for a translating finger. The sidebranching instability is related to a single discrete oscillatory mode about the selected velocity solution, and the existence of a critical anisotropy is shown to be due to the zero crossing of its growth rate. The marginal-stability hypothesis cannot predict the correct dynamics of this model system. We give heuristic arguments that the same ideas will apply to dendritic growth in the full diffusion system.

A method is presented for calculating the rates of activated processes when the preconditions for the use of Brownian-motion theory are not met. Use of this theory requires the existence of a separation of time scales of bath and reactant motions: That of the bath must be much more rapid than that of the reactants. This results in quasiequilibrium. In the absence of such a time-scale separation, it is argued that rates are more correctly obtained by examination of the frequency at which instabilities are produced in the normal-mode spectrum of the system. Instabilities are the result of random modulation of certain parameters in the problem which is made manifest by retention of selected anharmonic terms in the potential energy of the system under investigation. Here, a calculation is made of the rate at which a particle leaves a self-adsorbed position on the surface of a solid, which is the rate-limiting step for the process of sublimation. This rate has the form of an Arrhenius law and the effective activation energy may be compared to that obtained by the use of absolute rate theory (ART). If the linear coupling at the surface is large compared to that in the bulk (or if the adsorbed particle’s mass is smaller than that of the substrate particles) the effect of the adsorbed particle, in the harmonic approximation, is to induce a local mode. In this case, the result of the method presented here differs greatly from that of ART, which predicts a rate which is far too high. However, when the coupling at the surface is comparable to or less than that in the bulk, there is close agreement between the two methods. It is thus concluded that absolute rate theory should work well for processes involved in sublimation.

The relativistic modulational instability of an intense circularly polarized electromagnetic wave propagating along an external magnetic field in a plasma is investigated. The method of investigation is based on the derivation of a nonlinear Schrödinger equation. The effect of the external magnetic field is to diminish the modulational instability of the circularly polarized wave. Actually, the modulational instability can be completely eliminated if the external magnetic field is sufficiently strong.

A thermal-neutron scattering experiment on dense hydrogen gas at 120 K and 730 bar reveals that the measured incoherent dynamic structure factor is consistent with the predictions derived from the mode-coupling theory up to wave numbers of about 1 A${̊}^{\mathrm{-}1}$.

The time evolution of an unstable quantum system in terms of the dynamical semigroup is described. Using the canonical decomposition theorem, the evolution semigroup is uniquely split into unitary and completely nonunitary parts. This feature provides a natural superselection principle. An association is then made of the evolution of the steady-state density matrix with the unitary part and that of the decaying-state density matrix with the completely nonunitary part. Thus the reversible dynamics goes with the unitary evolution and the irreversible one with the completely nonunitary evolution. A discussion of the von Neumann entropy of this system is also presented. It is shown that for long times, this entropy settles to a constant value different from the initial entropy. A simple example of an exponentially decaying state is discussed.

The problem of metastability due to quantum and thermal fluctuations in a weakly damped system is treated within Feynman’s influence-functional theory. It is shown that quite generally the nonequilibrium density matrix may be written as a single path integral. For a cubic metastable potential it has the form of a Feynman propagator with a complex Lagrangian containing second-order derivatives in time and terms noninvariant under time reversal. Dissipative tunneling and thermal activation emerge together as different solutions of the associated Lagrange equations. The low-temperature correction to the exponent of the tunneling rate behaves as $T^{n+1\mathrm{}}$ for a spectrum of bath excitations vanishing as ${\omega }^n$. It is shown, moreover, how this result may be understood in terms of environment-assisted tunneling. Thus the low-temperature behavior of the tunneling rate provides a method to measure the dissipation mechanism in the quantum regime.

The form of solitary waves in the one-dimensional diatomic lattice with anharmonic nearest-neighbor interactions has been found within a quasicontinuum approximation. These supersonic compression waves arise under the same very general conditions as in the monatomic lattice, but differ slightly in form. Numerical simulations demonstrate the solitonlike stability properties of these waves.

The authors present a self-consistent approximation scheme for the calculation of the dynamical polarizability α(k→,ω) and plasmon dispersion at long wavelengths in electron films trapped on the free surface of liquid helium. The principal building blocks to the construction of the approximation scheme are the nonlinear fluctuation-dissipation theorem and linearized equations for the plasma density, fluid velocity, pressure tensor, and heat-flow tensor moments. Equilibrium three-point correlations, quadratic polarizability response functions, and the Navier-Stokes hypothesis linking the pressure tensor to its trace are all central elements in the development of the theory. At frequencies high compared with the collision frequency, the Golden-Lu (GL) formula for α(k→,ω) exactly satisfies the ${\omega }^{\mathrm{-}4}$ moment sum rule. Analysis of ${\alpha }_{\mathrm{GL}(\mathrm{k}\to }$,ω) at ω≃(2π${\mathrm{ne}}^2$k/m${)}^{1/2}$≫${\mathrm{kv}}_{\mathrm{th}}$ leads to the description of the long-wavelength plasmon structure over the range of couping strengths spanning the entire fluid regime. The GL theory predicts that the transition from plasmonlike to longitudinal-phonon-like dispersion occurs at the critical value of the coupling parameter ${\Gamma }_{\mathrm{crit}}$=3.22; this transition is inextricably linked to the onset of a ‘‘liquid-state’’ short-range order signaled by the development of oscillations in the equilibrium pair correlation function somewhere in the range 2.2<Γ<2.9. In the infinite coupling (Γ→∞) limit, the GL long-wavelength dispersion relation very nearly reproduces the zero-temperature Bonsall-Maradudin longitudinal-phonon dispersion for the two-dimensional hexagonal lattice.

We present Monte Carlo simulations on a two-dimensional (2D) fluid of N infinitely thin hard rods of length L (N≤3200). This system has an isotropic phase at low densities and a ‘‘nematic’’ phase at high densities. Although true long-range orientational order is not excluded a priori, the simulations indicate that the nematic phase has algebraic order. We find no evidence for a first-order isotropic-nematic transition; rather, all the available evidence points towards the occurrence of a disclination-unbinding transition of the Kosterlitz-Thouless type. The heat capacity $C_P$ peaks at a density some 20% below the estimated disclination-unbinding transition point. We discuss earlier simulations on 2D nematics in the light of the current results. We have computed the virial coefficients of the hard-needle fluid up to $B_5$ and find that $B_4$ is very small, while $B_5$ is negative.

Following the ideas of Herzfeld, Rice, Fixman, and Mistura, we are able to establish the adiabatic temperature oscillations as the sole origin of the critical attenuation and dispersion near the consolute point of a binary liquid. Special attention is given to the scaling function F(Ω) for the attenuation normalized to its consolute-point value, where Ω is the frequency, scaled by the relaxation rate of the fluid. By imposing some general conditions, we are led to the empirical function F(Ω)=(1+${\Omega }^{\mathrm{-}1/2}$${)}^{\mathrm{-}2}$, which is in excellent agreement with the data of Garland and Sanchez. By including a new hydrodynamic effect, we find that the frequency scale is also in accord with experiment.

A theory of electron diffusion in a gas in the presence of an intense radiation field is presented. The theory is applicable when the classical electron oscillation energy ${\epsilon }_0$ exceeds the typical electron-gas inelastic collision energy loss ξ and when the frequency ω of the wave is much larger than the inelastic collision frequency ${\nu }_{\mathrm{coll}}$. It is shown that the existence of these two different time scales allows us to derive a simple Langevin type, model stochastic equation, describing the slow-time-scale electron transport in the gas. Assuming linear dependence of ${\nu }_{\mathrm{coll}}$ on the electron energy, simple analytic expressions for the time evolution of the average electron translational energy W and random-walk parameter 〈$x^2$${〉}_{\mathrm{av}}$ are derived. In the long-time limit W=ξ/4 and 〈$x^2$${〉}_{\mathrm{av}=\mathrm{Dt}}$, where the diffusion coefficient D is independent of both ω and ${\epsilon }_0$. These predictions are in a good agreement with the results of Monte Carlo computer experiments, conducted for the cases of ${\mathrm{N}}_2$ and Hg.

The Privman-Fisher hypothesis on the singular part of the free-energy density of a finite system, near the bulk critical point T=$T_c$, is examined in the context of an ideal relativistic Bose gas confined to a cuboidal enclosure ($L_1$×$L_2$×$L_3$) under periodic boundary conditions. Taking into account the possibility of particle-antiparticle pair production in the system, explicit expressions are derived for the free energy, the specific heat, and the condensate density at temperatures close to $T_c$, and the special cases of a cube, a square channel and a film are investigated at length. The various predictions of the Privman-Fisher hypothesis are fully borne out and the scaling functions governing the critical behavior of the system are found to be universal—irrespective of the severity of the relativistic effects. The influence of the latter enters only through the nonuniversal scale factors, $C_1$ and $C_2$, which depend on the particle mass m and density ρ as well.

The different possible wetting regimes occurring at a model semipermeable membrane (which separates a binary system into two fluid mixtures) are analyzed in the space of temperature T, membrane field ${\epsilon }_1$, and the chemical potential of the constrained species ${\mu }_2^{\mathrm{-}}$. We focus attention on the effect that the distance (in thermodynamic space) of the two bulk states has on the nature of the membrane interfacial transitions. The departures encountered from the wetting behavior for fluid-to-wall and fluid-fluid interfaces are emphasized.

We discuss apparent and real 1/$f^{\delta }$ divergencies in the small-frequency limit of power spectra of dynamical systems. Apparent 1/$f^2$ divergencies appear in ‘‘type-I’’ intermittency and whenever there is infrequent random hopping between regions with chaotic motion. Real 1/$f^{\delta }$ divergencies appear in ‘‘types-II and -III’’ intermittency. The universal properties of these divergencies are discussed in the context of one- and two-dimensional maps.