In a recent paper [N. R. Corngold Phys. Rev. A 39, 2126 (1989)] it has been stated that collision cascades produced by soft power-law potentials do not conserve energy. In this paper it is shown that this fact is an artificial paradox caused by the incorrect treatment of a singular point of the collision integral of the Boltzmann equation. The exact solution, which obeys energy conservation, of the Boltzmann equation is presented, and properties of the cascade model used in Corngold’s paper are discussed.

I respond to the preceding Comment [Phys. Rev. A 41, 7070 (1990)] by D. L. Maslov.

The equivalence between a recently studied generalized restricted solid-on-solid growth model and the corresponding continuum equation is discussed. It is shown that the unusual behavior observed in this model is due to a crossing of the corresponding nonlinearity parameter in the continuum equation from negative to positive values. The observed critical point where logarithmic (Edwards-Wilkinson) behavior was observed corresponds to the point at which this parameter vanishes. Monte Carlo simulations for the growth velocity as a function of overall interface tilt lend support to this idea.

One-dimensional systems driven by colored external noise are studied in the weak-noise limit. The steepest-descent approximation is employed to obtain the stationary probability distribution in two-dimensional space. The approach is expected to be applicable to a large class of two-dimensional Fokker-Planck equations with noninvertible diffusion. A systematical expansion to improve the steepest-descent approximation is suggested.

We study growing interfaces in two- and three-dimensional systems by the numerical integration of the Kardar-Parisi-Zhang equation and the Monte Carlo simulation of a solid-on-solid model with asymmetric rates of evaporation and condensation. A crossover scaling ansatz is proposed, which we find accounts for the dependence of growth on the driving force, as we crossover from the dynamic roughening regime, where that force is identically zero, to driven growth, where a nonzero driving force is present. We thus estimate the crossover scaling exponents, as well as the scaling functions.

A cellular-automaton model of threshold elements with deterministic dynamics is introduced. The model is a cellular-automaton version of the mechanical earthquake model invented originally by Burridge and Knopoff [Bull. Seismol. Soc. Am. 57, 341 (1967)] and studied recently by Carlson and Langer [Phys. Rev. Lett. 62, 2632 (1989); Phys. Rev. A 40, 6470 (1989)]. Randomness exists only in initial configurations. Numerical results show that the distribution function of the event magnitudes has a scaling region consistent with the Gutenberg-Richter law.

We report results on the dynamics of a moving nematic-isotropic interface. Using thinner samples, the restabilization back to a linear interface at large velocities is observed. This allows a study of the full marginal stability curve, defining a tongue in the relevant parameter space. In this tongue many bifurcations exist. Close to the marginal stability line, sources, sinks, and traveling waves are observed in this system.

A unified density-functional theory for classical nonuniform systems is proposed. The theory is based on mapping the excess free energy of a nonuniform system onto that of an effective liquid; in the uniform limit, the theory reproduces the known properties of the liquid. Connection with previous density-functional theories is also established. Finally, the theory is applied to the freezing of the hard-sphere liquid, giving results in good agreement with computer simulations.

Learning from examples by a perceptron with binary synaptic parameters is studied. The examples are given by a reference (teacher) perceptron. It is shown that as the number of examples increases, the network undergoes a first-order transition, where it freezes into the state of the reference perceptron. When the transition point is approached from below, the generalization error reaches a minimal positive value, while above that point the error is constantly zero. The transition is found to occur at ${\mathrm{\alpha }}_{\mathrm{GD}}$=1.245 examples per coupling [E. Gardner and B. Derrida, J. Phys. A 22, 1983 (1989)].

The techniques of group-theoretical statistical mechanics (GTSM) are applied to various aspects of the interaction of electromagnetic radiation with molecular ensembles. Six nonlinear optical effects are examined in terms of the three principles of GTSM, using a classical series expansion of the induced electric dipole moment in terms of the electric and magnetic components of the electromagnetic field. Classical-quantum equivalence relations are derived at each stage. Symmetry arguments are applied to the chiral properties of some of the new nonlinear optical effects using the third principle of GTSM. A careful distinction is made between natural and magnetic optical activity, and our analysis attempts to resolve some recent disagreements in the literature.

Within the framework of thermo-field-dynamics, we define the reduced probability densities, and investigate the sum of information-theoretic entropies in quantum mechanics associated with the measurements of the position and momentum of a particle surrounded by the thermal environment. It is found that this quantity cannot be made arbitrarily small but has a universal lower bound dependent on the temperature. We develop the finite-temperature variational technique for the reduced system, and show that this relation, termed the thermal information-entropic uncertainty relation, is exactly saturated by the thermal coherent state. We also show that the Heisenberg uncertainty relation at finite temperature can be derived from this relation.

The Husimi distribution for the eigenstates of a classically nonintegrable two-dimensional system with mixed phase space was calculated in order to analyze its structure in terms of classical trajectories. Besides eigenfunctions concentrated on invariant tori or with support on chaotic regions of phase space, we also found others that combine different classical invariant sets (like a stable and an unstable periodic orbit) and families of eigenstates scarred by classically unstable periodic orbits.

Multimode squeeze and rotation operators are defined such that they have extremely similar algebraic properties as those of their single-mode counterparts. It is shown that the introduction of N-mode squeeze operators provides a convenient set of parameters to describe the variances of the quadrature amplitudes in multimode Gaussian squeezed states. Some important properties of these N-mode unitary operators are investigated. It is also shown that the time-evolution operator for a general N-mode quadratic Hamiltonian can be conveniently expressed as an operator product containing an N-mode squeeze operator, an N-mode rotation operator, and an N-mode displacement operator.

The frequencies of four ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}_2^{}{}_{}{}^{}$ transitions at 486 nm, which are of interest as references in precision measurements of the 1S-2S transitions in hydrogen, deuterium, and positronium, are determined with an accuracy of 1 part in ${10}^9$ by interferometric comparison with ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}_2^{}{}_{}{}^{}$ standard transitions.

A critical review of Casimir forces and their various interpretations is given. The Casimir effect for the case of dielectric slabs is studied in detail. The electromagnetic field is quantized in the presence of dielectric material and the notion of physical photons is introduced. The Casimir force originates from the pressure of the electromagnetic field in the vacuum state on the slab and is calculated with the help of the Maxwell stress tensor. It is shown that the Casimir force depends in a simple way on the mode density of the electromagnetic field. The dependence of the Casimir force on the reflection coefficient and the plate thickness is found.

The Hamiltonian of a quantum-mechanical system contains a time-dependent parameter X. The system is prepared in a highly excited eigenstate of the instantaneous Hamiltonian at t=0, and we compute the amplitudes 〈n(t)‖ψ(t)〉 to be in the eigenstates ‖n〉 of the instantaneous Hamiltonian H^(X(t)) at later times. It is found that for generic systems, with no symmetries yielding additional quantum numbers, the occupation probability spreads diffusively away from the initial state. This diffusion is an irreversible process, and can be related to a model for dissipation. The diffusion constant D is investigated numerically in a random matrix model as a function of Ẋ, the rate of change of the parameter. Good agreement with theoretical predictions is found in two limiting regimes. When Ẋ is large, D is proportional to Ẋ ${}_{}{}^2{}_{}{}^{}$, corresponding to the Ohmic dissipation predicted by the Kubo formula. When Ẋ is small, Landau-Zener transitions are the mechanism for diffusion, and D is proportional to Ẋ ${}_{}{}^{3/2}{}_{}{}^{}$.

For an electron gas in a uniform magnetic field, explicit expressions of the electron density, current density, and the density matrix are derived as functions of the Fermi energy and the field strength, using plane waves and the Landau energy levels. The local-density approximations for the kinetic and the exchange energy functionals for an inhomogeneous many-electron system are thereby suggested using the density quantities as basic variables. A practical scheme for the density-functional calculation involving the magnetic field in the spirit of Thomas-Fermi-Dirac theory is outlined.

A calculation of the magnetic dipole transition 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$–1 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ in heliumlike argon is presented. The calculation is performed in a relativistic framework and includes the Coulomb interaction, in the no-virtual-pair approximation, to all orders. Contributions from the exchange of virtual photons, i.e., from the Breit interaction, are of the same formal order of magnitude as contributions from the Coulomb interaction and are treated on the same footing. The combination of a relativistic treatment and the inclusion of correlation in the calculation results in an improved accuracy compared with previous calculations. The lifetime of the 2${\mathrm{}}^3$${\mathit{S}}_1$ state is predicted to be 209.4±0.4 nsec, which includes an estimate of neglected effects, ±0.2 nsec, and numerical errors, ±0.2 nsec. This result agrees with experiment, 202±12 nsec, within present error bars. A detailed breakdown of the contributions to the transition energy is also presented. The contribution to the ground-state energy of ${\mathrm{Ar}}^{16+}$ from the mixture of the Breit and the Coulomb interaction is calculated to all orders. This contribution is 9% smaller than the result in the Pauli approximation.

An implementation of the coupled-cluster single- and double-excitation (CCSD) method is presented. The CCSD equations are expressed in form of a system of coupled one-particle and two-particle equations. The complete expressions of these equations in terms of Goldstone diagrams are given. Also presented is a simplified diagrammatic notation corresponding to an efficient evaluation scheme. By using numerical discrete spectra to solve these equations, a high numerical accuracy, better than 1 μhartree, is obtained. The method is tested on Be and ${\mathrm{Li}}^{\mathrm{-}}$ and is found to account for 99.3% and 99.4% of the correlation energy, respectively. The CCSD method is demonstrated to give total energies depending very little on the potential used to define the perturbation expansion.