The formalism necessary to understand the phenomenon of $\mathrm{CP}$ nonconservation as observed in the neutral-kaon system is presented. The distinction between indirect $\mathrm{CP}$ violation and direct $\mathrm{CP}$ violation is made, and the level of understanding of the phenomenon in the standard model is reviewed. Attention is placed on new experimental efforts that could definitely establish a first-order or direct effect. The authors analyze the potential for such an observation in both kaon and $B$-meson decays and give the range of predictions from the standard model. Other possible models are considered briefly.

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector $q_0$ and frequency ${\omega }_0$ of the instability. Type ${\mathrm{I}}_{\mathrm{s}}$ systems (${\omega }_0=0\mathrm{}$, $q_0\ne 0$) are stationary in time and periodic in space; type ${\mathrm{III}}_{\mathrm{o}}$ systems (${\omega }_0\ne 0$, $q_0=0\mathrm{}$) are periodic in time and uniform in space; and type ${\mathrm{I}}_{\mathrm{o}}$ systems (${\omega }_0\ne 0$, $q_0\ne 0$) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Bénard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

It is an open question whether the slow dynamics of spin glasses is more accurately described by a model based on rather compact droplets which can flip thermally, or by a picture of more diffuse sets of flipping spins with properties described by hierarchical dynamics. Techniques have been developed for analyzing spontaneous fluctuations in mesoscopic samples which can directly address this question. In a well-known spin glass, $\mathrm{Cu}\mathrm{Mn}$, the experimental results are better fit by the hierarchical picture. Previously unexplored properties of the space of metastable configurations are directly measurable by these mesoscopic methods.

The authors review theoretical estimates of spatial, spin, and isospin correlations among the nucleons in nuclei. The momentum distribution and spectral function of nucleons in nuclei are also discussed. The theoretical estimates are compared with the observed correlation effects in the inclusive scattering of electrons from nuclei, at energies ranging from a few hundred MeV to several GeV. The observed transparencies of nuclei to protons ejected in inclusive $e$,$e^{\prime }p$ reactions are also compared with their theoretical estimates. Finally, the quenching of exclusive single-quasiparticle-type reactions, indicative of the overall strength of correlations in nuclei, is discussed. There appears to be a qualitative agreement between theory and experiment, but a firm quantitative understanding is still to be obtained.

Although skeptical of the prohibitive power of no-hidden-variables theorems, John Bell was himself responsible for the two most important ones. I describe some recent versions of the lesser known of the two (familiar to experts as the "Kochen-Specker theorem") which have transparently simple proofs. One of the new versions can be converted without additional analysis into a powerful form of the very much better known "Bell's Theorem," thereby clarifying the conceptual link between these two results of Bell.

The main purpose of this paper is to further our theoretical understanding of the fractional quantum Hall effect, in particular of spin effects, in two-dimensional incompressible electron fluids subject to a strong, transverse magnetic field. As a prerequisite for an analysis of the quantum Hall effect, the authors develop a general formulation of the many-body theory of spinning particles coupled to external electromagnetic fields and moving through a general, geometrically nontrivial background. Their formulation is based on a Lagrangian path-integral quantization and is valid in arbitrary coordinates, including coordinates moving according to a volume-preserving flow. It is found that nonrelativistic quantum theory exhibits a fundamental, local U(1)×SU(2) gauge invariance, and the corresponding gauge fields are identified with physical, external fields. To illustrate the usefulness of their formalism, the authors prove a general form of the quantum-mechanical Larmor theorem and discuss some well-known effects, including the Barnett-Einstein-de Haas effect and superconductivity, emphasizing the implications of U(1)×SU(2) gauge invariance. They then consider two-dimensional, incompressible quantum fluids in more detail. Exploiting U(1)×SU(2) gauge invariance, they calculate the leading terms in the effective actions of such systems as functionals of the U(1) and SU(2) gauge fields, on large-distance and low-frequency scales. Among the applications of these results are a simple proof of the Goldstone theorem for spin waves and the linearresponse theory of two-dimensional, incompressible Hall fluids, including a Hall effect for spin currents and sum rules for the response coefficients. For two-dimensional, incompressible systems with broken parity and time-reversal symmetry, a particularly significant implication of U(1)×SU(2) gauge invariance is a duality between the physics inside the bulk of the system and the physics of gapless, chiral modes propagating along the boundary of the system. These modes form chiral $\hat{\mathrm{u}}\mathrm{}\left(1\right)\mathrm{}$ and $\mathrm{s}\hat{\mathrm{u}}\mathrm{}\left(2\right)\mathrm{}$ current algebras. The representation theory of these current algebras, combined with natural physical constraints, permits one to derive the quantization of the response coefficients, such as the Hall conductivity. A classification of incompressible Hall fluids is outlined, and many examples, including one concerning a superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$\frac{A}{B}$ interface, are discussed.

The jellium model of simple metal clusters has enjoyed remarkable empirical success, leading to many theoretical questions. In this review, we first survey the hierarchy of theoretical approximations leading to the model. We then describe the jellium model in detail, including various extensions. One important and useful approximation is the local-density approximation to exchange and correlation effects, which greatly simplifies self-consistent calculations of the electronic structure. Another valuable tool is the semiclassical approximation to the single-particle density matrix, which gives a theoretical framework to connect the properties of large clusters with the bulk and macroscopic surface properties. The physical properties discussed in this review are the ground-state binding energies, the ionization potentials, and the dipole polarizabilities. We also treat the collective electronic excitations from the point of view of the cluster response, including some useful sum rules.

The study of simple metal clusters has burgeoned in the last decade, motivated by the growing interest in the evolution of physical properties from the atom to the bulk solid, a progression passing through the domain of atomic clusters. On the experimental side, the rapid development of new techniques for producing the clusters and for probing and detecting them has resulted in a phenomenal increase in our knowledge of these systems. For clusters of the simplest metals, the alkali and noble metals, the electronic structure is dominated by the number of valence electrons, and the ionic cores are of secondary importance. These electrons are delocalized, and the electronic system exhibits a shell structure that is closely related to the well-known nuclear shell structure. In this article the results from a broad range of experiments are reviewed and compared with theory. Included are the behavior of the mass-abundance spectra, polarizabilities, ionization potentials, photoelectron spectra, optical spectra, and fragmentation phenomena.

The role played by dynamic symmetries and supersymmetries in nuclear physics is described and interpreted with experimental examples. Implications for other fields of physics are reviewed briefly.

Theory and experiment have revealed that novel behavior occurs when a Cs surface is exposed to ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ vapor. For temperature $T$ below the wetting temperature ($T_w\simeq 2$ K), ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ forms only a microscopically thin film as the vapor pressure $P$ increases from zero to its saturated value. For intermediate values of $T \left(T_w\le T\le T_c\simeq 2.5 \mathrm{K}\right)$, the film thickness jumps discontinuously at a prewetting transition pressure $P_{\mathrm{pw}}\mathrm{}\left(T\right)\mathrm{}$. For $P>\mathrm{}{P}_{\mathrm{pw}}$, and for all $P$ if $T>\mathrm{}{T}_c$, the film grows continuously to infinite thickness as saturation is approached. Microscopic theories of these phenomena are discussed in terms of the basic physics of electrons and atomic interactions. Initial experimental observations are summarized. Related phenomena of interest are described, including observation of prewetting with adsorbates other than He and substrates other than Cs.

A summary is presented of the statistical mechanical theory of learning a rule with a neural network, a rapidly advancing area which is closely related to other inverse problems frequently encountered by physicists. By emphasizing the relationship between neural networks and strongly interacting physical systems, such as spin glasses, the authors show how learning theory has provided a workshop in which to develop new, exact analytical techniques.

Magnetoencephalography (MEG) is a noninvasive technique for investigating neuronal activity in the living human brain. The time resolution of the method is better than 1 ms and the spatial discrimination is, under favorable circumstances, 2-3 mm for sources in the cerebral cortex. In MEG studies, the weak 10 fT-1 pT magnetic fields produced by electric currents flowing in neurons are measured with multichannel SQUID (superconducting quantum interference device) gradiometers. The sites in the cerebral cortex that are activated by a stimulus can be found from the detected magnetic-field distribution, provided that appropriate assumptions about the source render the solution of the inverse problem unique. Many interesting properties of the working human brain can be studied, including spontaneous activity and signal processing following external stimuli. For clinical purposes, determination of the locations of epileptic foci is of interest. The authors begin with a general introduction and a short discussion of the neural basis of MEG. The mathematical theory of the method is then explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices. Finally, several MEG experiments performed in the authors' laboratory are described, covering studies of evoked responses and of spontaneous activity in both healthy and diseased brains. Many MEG studies by other groups are discussed briefly as well.

Molecular-beam experiments have exposed a new wealth of detail on the general reaction $A^{*}+B\to A+B^{+}+e^{-}$ first suggested by Penning in 1927. The new capabilities not available to traditional swarm techniques include mass and electron spectroscopy on the reaction products and angle-resolved measurements of the scattering of both reagents and products. These new results have stimulated the recent development of both the electronic structure and the dynamical theories necessary for a first-principles description of at least the simplest of these reactions, those involving small atomic and diatomic species $B$. Recent progress in both experiment and interpretation is critically reviewed, and the prospects for attaining a global understanding of Penning ionization in larger systems are assessed.

This review summarizes the current status of both brown dwarf theory and the searches for these elusive substellar objects. The conceptual continuity between the brown dwarf and the well-studied M dwarf branches is emphasized throughout. The physics of their atmospheres and interiors is reviewed and an analytic model of both brown dwarf evolution and the lower edge of the hydrogen main sequence is presented. An extensive discussion of brown dwarf searches in the field, in binaries, around white dwarfs, in clusters, in the solar neighborhood, in the galactic halo, and using proper-motion catalogs is provided, as is a tentative list of candidates in the field. The theory near and below the edge of the main sequence, while sophisticated, is only now being successfully challenged by optical and infrared observations. The near future promises a productive explosion in our knowledge of this problematic galactic population.

The review begins by grouping the fundamental nuclear reactions into two classifications, namely, the usual binary processes and few-particle processes. In the few-particle processes, the possibility of electron-screened cold fusion is remarked. The special features of dense plasmas rest in the enhancement of reaction rates over these fundamental processes due to internuclear many-particle processes. The manyparticle processes arise from a modification of the short-range correlations between reacting nuclei and are the effects related closely to differences between Coulombic chemical potentials before and after the nuclear reactions. Quantum statistical-mechanical formulation of the enhancement factors is presented. Thermodynamic functions for various realizations of dense plasmas, pertinent directly to the reaction-rate theories through the screening properties and free energies, are summarized. Those analyses are then applied to the estimation of nuclear reaction rates in specific examples of dense astrophysical plasmas, namely, the Sun, brown dwarfs, giant planets, white-dwarf progenitors of supernovae, and helium burning on the degenerate stars, as well as in those dense laboratory plasmas that are found in the inertial confinement fusion experiments, in metal hydrides such as PdD and Ti${\mathrm{D}}_2$, in cluster-impact fusion experiments, and in ultrahigh-pressure liquid metals. The essential similarity between the nuclear fusion reactions in supernovae and those projected in the ultrahigh-pressure liquid metals is particularly emphasized.