Topological methods have recently been developed for the analysis of dissipative dynamical systems that operate in the chaotic regime. They were originally developed for three-dimensional dissipative dynamical systems, but they are applicable to all “low-dimensional” dynamical systems. These are systems for which the flow rapidly relaxes to a three-dimensional subspace of phase space. Equivalently, the associated attractor has Lyapunov dimension $d_L<3.\mathrm{}$ Topological methods supplement methods previously developed to determine the values of metric and dynamical invariants. However, topological methods possess three additional features: they describe how to model the dynamics; they allow validation of the models so developed; and the topological invariants are robust under changes in control-parameter values. The topological-analysis procedure depends on identifying the stretching and squeezing mechanisms that act to create a strange attractor and organize all the unstable periodic orbits in this attractor in a unique way. The stretching and squeezing mechanisms are represented by a caricature, a branched manifold, which is also called a template or a knot holder. This turns out to be a version of the dynamical system in the limit of infinite dissipation. This topological structure is identified by a set of integer invariants. One of the truly remarkable results of the topological-analysis procedure is that these integer invariants can be extracted from a chaotic time series. Furthermore, self-consistency checks can be used to confirm the integer values. These integers can be used to determine whether or not two dynamical systems are equivalent; in particular, they can determine whether a model developed from time-series data is an accurate representation of a physical system. Conversely, these integers can be used to provide a model for the dynamical mechanisms that generate chaotic data. In fact, the author has constructed a doubly discrete classification of strange attractors. The underlying branched manifold provides one discrete classification. Each branched manifold has an “unfolding” or perturbation in which some subset of orbits is removed. The remaining orbits are determined by a basis set of orbits that forces the presence of all remaining orbits. Branched manifolds and basis sets of orbits provide this doubly discrete classification of strange attractors. In this review the author describes the steps that have been developed to implement the topological-analysis procedure. In addition, the author illustrates how to apply this procedure by carrying out the analysis of several experimental data sets. The results obtained for several other experimental time series that exhibit chaotic behavior are also described.

Interferometry at radio frequencies between Earth-based receivers separated by intercontinental distances has made significant contributions to astrometry and geophysics during the past three decades. Analyses of such very long baseline interferometric (VLBI) experiments now permit measurements of relative positions of points on the Earth’s surface and of angles between celestial objects at levels of better than one cm and one nanoradian, respectively. The relative angular positions of extragalactic radio sources inferred from this technique presently form the best realization of an inertial reference frame. This review summarizes the current status of radio interferometric measurements for astrometric and geodetic applications. It emphasizes the theoretical models that are required to extract results from the VLBI observables at present accuracy levels. An unusually broad cross section of physics contributes to the required modeling. Both special and general relativity need to be considered in properly formulating the geometric part of the propagation delay. While high-altitude atmospheric charged-particle (ionospheric) effects are easily calibrated for measurements employing two well-separated frequencies, the contribution of the neutral atmosphere at lower altitudes is more difficult to remove. In fact, mismodeling of the troposphere remains the dominant error source. Plate tectonic motions of the observing stations need to be taken into account, as well as the nonpointlike intensity distributions of many sources. Numerous small periodic and quasiperiodic tidal effects also make important contributions to space geodetic observables at the centimeter level, and some of these are just beginning to be characterized. Another area of current rapid advances is the specification of the orientation of the Earth’s spin axis in inertial space: nutation and precession. Highlights of the achievements of very long baseline interferometry are presented in four areas: reference frames, Earth orientation, atmospheric effects on microwave propagation, and relativity. The order-of-magnitude improvement of accuracy that was achieved during the last decade has provided essential input to geophysical models of the Earth’s internal structure. Most aspects of VLBI modeling are also directly applicable to interpretation of other space geodetic measurements, such as active and passive ranging to Earth-orbiting satellites, interplanetary spacecraft, and the Moon.

Neutrino-scattering measurements offer a unique tool for probing the electroweak and strong interactions as described by the standard model. Electroweak measurements are accessible through the comparison of neutrino neutral- and charged-current scattering. These measurements are complementary to other electroweak measurements due to differences in the radiative corrections both within and outside the standard model. Neutrino-scattering measurements also provide a precise method for measuring the $F_2{(x,Q}^2)$ and ${\mathrm{xF}}_3{(x,Q}^2)$ structure functions. The predicted ${\mathrm{Q}}^2$ evolution can be used to test perturbative quantum chromodynamics as well as to measure the strong-coupling constant ${\alpha }_s$ and the valence, sea, and gluon parton distributions. In addition, neutrino charm production, which can be determined from the observed dimuon events, allows the strange-quark sea to be investigated along with measurements of the CKM matrix element $|V_{\mathrm{cd}}|$ and the charm quark mass.

This report reviews the achievements of the Crystal Barrel experiment at the Low-Energy Antiproton Ring (LEAR) at CERN. During seven years of operation Crystal Barrel has collected very large statistical samples in $\overline{p}p$ annihilation, especially at rest and with emphasis on final states with high neutral multiplicity. The measured rates for annihilation into various two-body channels and for electromagnetic processes have been used to test simple models for the annihilation mechanism based on the internal quark structure of hadrons. The production of $\phi$ mesons is larger than predicted in several annihilation channels. Important contributions to the spectroscopy of light mesons have been made. The exotic $\rho ̂\mathrm{}\left(1405\right)\mathrm{}$ meson with quantum numbers $J^{\mathrm{PC}}{=1\mathrm{}}^{-+}$ has been observed in its $\eta \pi$ decay mode. Two $2^{-+}$ isoscalar mesons ${\eta }_2\mathrm{}\left(1645\right)\mathrm{}$ and ${\eta }_2\mathrm{}\left(1870\right),$ and the $0^{-+}$ isoscalar meson $\eta \mathrm{}\left(1410\right)\mathrm{}$ have been observed in the $\eta \pi \pi$ decay channel. From three-body annihilations three $0^{++}$ mesons, $a_0\mathrm{}\left(1450\right),$ $f_0\mathrm{}\left(1370\right),$ and $f_0\mathrm{}\left(1500\right)\mathrm{}$ have been established in various decay modes. One of them, $f_0\mathrm{}\left(1500\right),$ may be identified with the expected ground-state scalar glueball.

We review and analyze the available information on the nuclear-fusion cross sections that are most important for solar energy generation and solar neutrino production. We provide best values for the low-energy cross-section factors and, wherever possible, estimates of the uncertainties. We also describe the most important experiments and calculations that are required in order to improve our knowledge of solar fusion rates.

Metal-insulator transitions are accompanied by huge resistivity changes, even over tens of orders of magnitude, and are widely observed in condensed-matter systems. This article presents the observations and current understanding of the metal-insulator transition with a pedagogical introduction to the subject. Especially important are the transitions driven by correlation effects associated with the electron-electron interaction. The insulating phase caused by the correlation effects is categorized as the Mott Insulator. Near the transition point the metallic state shows fluctuations and orderings in the spin, charge, and orbital degrees of freedom. The properties of these metals are frequently quite different from those of ordinary metals, as measured by transport, optical, and magnetic probes. The review first describes theoretical approaches to the unusual metallic states and to the metal-insulator transition. The Fermi-liquid theory treats the correlations that can be adiabatically connected with the noninteracting picture. Strong-coupling models that do not require Fermi-liquid behavior have also been developed. Much work has also been done on the scaling theory of the transition. A central issue for this review is the evaluation of these approaches in simple theoretical systems such as the Hubbard model and $t-J$ models. Another key issue is strong competition among various orderings as in the interplay of spin and orbital fluctuations. Experimentally, the unusual properties of the metallic state near the insulating transition have been most extensively studied in $d$-electron systems. In particular, there is revived interest in transition-metal oxides, motivated by the epoch-making findings of high-temperature superconductivity in cuprates and colossal magnetoresistance in manganites. The article reviews the rich phenomena of anomalous metallicity, taking as examples Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Ru compounds. The diverse phenomena include strong spin and orbital fluctuations, mass renormalization effects, incoherence of charge dynamics, and phase transitions under control of key parameters such as band filling, bandwidth, and dimensionality. These parameters are experimentally varied by doping, pressure, chemical composition, and magnetic fields. Much of the observed behavior can be described by the current theory. Open questions and future problems are also extracted from comparison between experimental results and theoretical achievements.

The techniques of quantum field theory on a lattice are used to examine the diffusion and reaction processes of particles in a solid, such as vacancies or interstitials, or chemical species of all kinds which move by discrete random hopping processes and react in a prescribed way when they are in proximity. First formulated by Doi in the 1970s, the quantum-field-theoretic solution of the “master equation” of statistical physics allows a systematic investigation of any number of nonequilibrium processes ranging from fluorescence to explosions. By formulating the problem on the points of a space lattice in $d$ dimensions one can control the ultraviolet divergences associated with short-range interactions. For illustrative purposes several models are solved in detail. The authors include as an appendix a chronological list of seminal articles in the field.

The diffusion of muons and muonium through solids has been studied over many years using the technique of spin relaxation. At low temperatures, the motion is due to tunneling between lattice sites, and the competition between tunneling rates and decoherence rates is important in determining the dynamics. Coherent propagation is seen in superconductors and insulators at low temperature where dissipation is small. At higher temperatures the motion undergoes a crossover from bandlike propagation to incoherent hopping between neighboring sites. This review covers both theory and experiment, emphasizing the mechanisms for dissipation, the role of barrier fluctuations, and effects of crystal disorder on the transport. The review of experimental data includes an analysis of barrier penetration bandwidths for muon and muonium diffusion in a variety of metals and insulators.

The authors review the results of a wide variety of experiments on materials such as ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$ that contain weakly coupled ${\mathrm{CuO}}_2$ layers. These materials are antiferromagnetic insulators with very large Heisenberg exchange energies, which become high-temperature superconductors when charge carriers are added to the ${\mathrm{CuO}}_2$ layers. The growth of large single crystals has made it possible to carry out neutron scattering, as well as anisotropic optical, transport, and magnetization measurements. The properties of the undoped ${\mathrm{CuO}}_2$ layer are reviewed, and the evolution of magnetic, optical, and transport properties with the addition of charge carriers is discussed. The emphasis is on the pure and lightly doped materials, although the magnetism in the superconductors is discussed.

A comprehensive review of the present understanding, both theoretical and experimental, of intrinsic and rotational level structures in medium-heavy deformed odd-odd nuclei is presented. A discussion of the various experimental methods is presented, emphasizing the need for a variety of experimental approaches. The odd-odd nuclei that are immediately amenable to fruitful additional study are pointed out. A discussion of the intrinsic level structures, Gallagher-Moszkowski (GM) splittings, Newby (N) shifts, and role of the residual $p-n$ interaction is presented. Currently available data in the rare-earth region allow the empirical determination of 137 GM splittings and 36 N shifts for 25 odd-odd nuclei in the mass region 152⩽$A$⩽188. A new parametrization of the residual $p-n$ interaction is presented which also takes into account the 27 GM splittings and 12 N shifts from the actinide region. Newly discovered features of rotational bands, such as odd-even staggering, and other high-spin phenomena, such as signature inversion and delay in bandcrossing frequency, are discussed. The role of higher-order Coriolis coupling is pointed out. Systematics of the two-quasiparticle excitations, shape coexistence, isomers, and four-quasiparticle states are presented. Calculated results of the two-quasiparticle intrinsic excitations using two methods, the intrinsic level spacings for odd-A neighboring nuclei and the quasiparticle-plus-phonon coupling model, are compared with experiment.

Few-nucleon physics is a field rich with high-quality experimental data and possibilities for accurate calculations of strongly correlated quantum systems. In this article the authors discuss the traditional model of the nucleus as a system of interacting nucleons and outline many recent experimental results and theoretical developments in the field of few-nucleon physics. The authors describe nuclear structure and spectra, clustering and correlations, elastic and inelastic electromagnetic form factors, low-energy electroweak reactions, and nuclear scattering and response in the quasielastic regime. Through a review of the rich body of experimental data and a variety of theoretical developments, a coherent description of the nuclear strong- and electroweak-interaction properties emerges. In this article, the authors attempt to provide some insight into the practice and possibilities in few-nucleon physics today.

At low light levels, the visual system detects and counts photon absorptions with a reliability close to limits set by statistical fluctuations in the number of absorbed photons. Thus the rod photoreceptors that provide the input signals to the dark-adapted visual system act as nearly perfect photon counters. This elegant performance is possible because light detection in the rods satisfies four functional requirements: high quantum efficiency, sufficient amplification to produce a measurable response, low dark noise, and low trial-to-trial variability in the elementary response. The rod meets these requirements using biochemical reactions rather than the solid-state reactions of silicon detectors, yet its performance equals or exceeds that of man-made detectors in several ways.

The authors discuss the technique of stimulated Raman adiabatic passage (STIRAP), a method of using partially overlapping pulses (from pump and Stokes lasers) to produce complete population transfer between two quantum states of an atom or molecule. The procedure relies on the initial creation of a coherence (a population-trapping state) with subsequent adiabatic evolution. The authors present the basic theory, with some extensions, and then describe examples of experimental utilization. They note some applications of the technique not only to preparation of selected states for reaction studies, but also to quantum optics and atom optics.

The nature and origins of renormalization group ideas in statistical physics and condensed matter theory are recounted informally, emphasizing those features of prime importance in these areas of science in contradistinction to quantum field theory, in particular: critical exponents and scaling, relevance, irrelevance and marginality, universality, and Wilson’s crucial concept of flows and fixed points in a large space of Hamiltonians.

This article explains how a simple equation describing the time evolution of a superfluid’s quantum phase can be used as a powerful tool to rapidly deduce exact magnitudes of physical observables in situations involving very complex vortex motion. The equation has been used to simplify the understanding of new phenomena, such as vortex precession. Applications of the equation have also led to solutions of long-standing problems, such as the nucleation of vortices, and to new technology, such as the superfluid gyroscope. The article begins by presenting some basic ideas of superfluidity. This discussion leads to the concept of the quantum phase of the superfluid state and to the prediction that vorticity is quantized. Next a discussion is presented of the phase evolution equation, introduced by Josephson and developed further by Anderson. The utility of the equation is demonstrated by making certain general predictions about the consequences of vortex motion. Two experiments, one in ${}^3\mathrm{He}$ and another in ${}^4\mathrm{He},$ are then described in the context of the phase evolution equation. In the first, the precession frequency of a single vortex filament is easily explained in the context of the equation. In the second, quantized dissipation processes are observed which give detailed information about the creation of quantized vortices. The article concludes by showing how these latter experiments have led to the development of a superfluid sensor of absolute rotation. Although the article focuses on results emerging from the author’s own laboratory, the footnotes lead the reader to some of the parallel ongoing projects, especially in the case of the ${}^4\mathrm{He}$ research at Orsay/Saclay in France, the University of Minnesota, and the University of Trento, Italy.

The daily motion of the Moon through the sky has many unusual features that a careful observer can discover without the help of instruments. The three different frequencies for the three degrees of freedom have been known very accurately for 3000 years, and the geometric explanation of the Greek astronomers was basically correct. Whereas Kepler’s laws are sufficient for describing the motion of the planets around the Sun, even the most obvious facts about the lunar motion cannot be understood without the gravitational attraction of both the Earth and the Sun. Newton discussed this problem at great length, and with mixed success; it was the only testing ground for his Universal Gravitation. This background for today’s many-body theory is discussed in some detail because all the guiding principles for our understanding can be traced to the earliest developments of astronomy. They are the oldest results of scientific inquiry, and they were the first ones to be confirmed by the great physicist-mathematicians of the 18th century. By a variety of methods, Laplace was able to claim complete agreement of celestial mechanics with the astronomical observations. Lagrange initiated a new trend wherein the mathematical problems of mechanics could all be solved by the same uniform process; canonical transformations eventually won the field. They were used for the first time on a large scale by Delaunay to find the ultimate solution of the lunar problem by perturbing the solution of the two-body Earth-Moon problem. Hill then treated the lunar trajectory as a displacement from a periodic orbit that is an exact solution of a restricted three-body problem. Newton’s difficultly in explaining the motion of the lunar perigee was finally resolved, and the Moon’s orbit was computed by a new method that became the universal standard until after WW II. Poincaré opened the 20th century with his analysis of trajectories in phase space, his insistence on investigating periodic orbits even in ergodic systems, and his critique of perturbation theory, particularly in the case of the Moon’s motion. Space exploration, astrophysics, and the landing of the astronauts on the Moon led to a new flowering of celestial mechanics. Lunar theory now has to confront many new data beyond the simple three-body problem in order to improve its accuracy below the precision of 1 arcsecond; the computer dominates all the theoretical advances. This review is intended as a case study of the many stages that characterize the slow development of a problem in physics from simple observations through many forms of explanation to a high-precision fit with the data.

Recent scientific and technical progress in magnetic fusion experiments has resulted in the achievement of plasma parameters (density and temperature) which made possible the production of significant bursts of fusion power from deuterium-tritium fuels and the first studies of the physics of burning plasmas. The key scientific issues in studying the reacting plasma core are plasma confinement, magnetohydrodynamic (MHD) stability, and the confinement and loss of energetic fusion products from the reacting fuel ions. Progress in the development of regimes of operation that both have good confinement and are MHD stable has made possible a broad study of problems in burning-plasma physics. The technical and scientific results from deuterium-tritium experiments on the Joint European Torus (JET) and the Tokamak Fusion Test Reactor (TFTR) are reviewed, with particular emphasis on alpha-particle physics issues.