The authors attempt to give a comprehensive discussion of observations of atomic negative-ion resonances throughout the periodic table. A review of experimental and theoretical approaches to the study of negative-ion resonances is given together with a consideration of the various schemes that are used for their classification. In addition to providing, where possible, tabulated data for the energies, widths, and symmetries of these states, the authors also attempt to highlight regularities in their behavior both within groups of the periodic table and along isoionic sequences.

The capacity $C$ of a communication channel is the maximum rate at which information can be transmitted without error from the channel's input to its output. The authors review quantum limits on the capacity that can be achieved with linear bosonic communication channels that have input power $P$. The limits arise ultimately from the Einstein relation that a field quantum at frequency $f$ has energy $E=hf$. A single linear bosonic channel corresponds to a single transverse mode of the bosonic field—i.e., to a particular spatial dependence in the plane orthogonal to the propagation direction and to a particular spin state or polarization. For a single channel the maximum communication rate is $C_{\mathrm{WB}}=\left(\frac{\pi }{\ln 2}\right)\sqrt{\frac{2P}{3h}}$ bits/s. This maximum rate can be achieved by a "number-state channel," in which information is encoded in the number of quanta in the bosonic field and in which this information is recovered at the output by counting quanta. Derivations of the optimum capacity $C_{\mathrm{WB}}$ are reviewed. Until quite recently all derivations assumed, explicitly or implicitly, a number-state channel. They thus left open the possibility that other techniques for encoding information on the bosonic field, together with other ways of detecting the field at the output, might lead to a greater communication rate. The authors present their own general derivation of the single-channel capacity upper bound, which applies to any physically realizable technique for encoding information on the bosonic field and to any physically realizable detection scheme at the output. They also review the capacities of coherent communication channels that encode information in coherent states and in quadrature-squeezed states. A three-dimensional bosonic channel can employ many transverse modes as parallel single channels. An upper bound on the information flux that can be transferred down parallel bosonic channels is derived.

Electron correlation plays an important role in determining the properties of physical systems, from atoms and molecules to condensed phases. Recent theoretical progress in the field has proven possible using both analytical methods and numerical many-body treatments, for realistic systems as well as for simplified models. Within the models, one may mention the jellium and the Hubbard. The jellium model, while providing a simple, rough approximation to conduction electrons in metals, also constitutes a key ingredient in the treatment of electrons in condensed phases within density-functional formalism. The Hubbard- and the related Heisenberg-model Hamiltonians, on the other hand, are designed to treat situations in which very strong correlations tend to bring about site localization of electrons. The character of the interactions in these lattice models allows for a local treatment of correlations. This is achieved by the use of projection techniques that were first proposed by Gutzwiller for the multicenter problem, being the natural extension of the Coulson-Fischer treatment of the ${\mathrm{H}}_2$ molecule. Much work in this area is analytic or semianalytic and requires approximations. However, a full many-body treatment of both realistic and simplified models is possible by resorting to numerical simulations, i.e., to the so-called quantum Monte Carlo method. This method, which can be implemented in a number of ways, has been applied to atoms, molecules, and solids. In spite of continuing progress, technical problems still remain. Thus one may mention the fermion sign problem and the increase in computational time with the nuclear charge in atomic and related situations. Still, this method provides, to date, one of the most accurate ways to calculate correlation energies, both in atomic and in multicenter problems.

This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous that focus is limited to a specific structure, the percolating network. Recent progress has followed three directions: scaling, numerical simulations, and experiment. In a happy coincidence, large-scale computations, especially those involving array processors, have become possible in recent years. Experimental techniques such as light- and neutron-scattering experiments have also been developed. Together, they form the basis for a review article useful as a guide to understanding these developments and for charting future research directions. In addition, new numerical simulation results for the dynamical properties of diluted antiferromagnets are presented and interpreted in terms of scaling arguments. The authors hope this article will bring the major advances and future issues facing this field into clearer focus, and will stimulate further research on the dynamical properties of random systems.

The interacting disordered electron problem is reviewed with emphasis on the quantum phase transitions that occur in a model system and on the field-theoretic methods used to describe them. An elementary discussion of conservation laws and diffusive dynamics is followed by a detailed derivation of the extended nonlinear sigma model, which serves as an effective field theory for the problem. A general scaling theory of metal-insulator and related transitions is developed, and explicit renormalization-group calculations for the various universality classes are reviewed and compared with experimental results. A discussion of pertinent physical ideas and phenomenological approaches to the metal-insulator transition not contained in the sigma-model approach is given, and phase-transition aspects of related problems, like disordered superconductors and the quantum Hall effect, are discussed. The review concludes with a list of open problems.

The account given here of the macroscopic and microscopic physical properties of antiferromagnetic (AFM) chromium alloys supplements the previous review of spin-density-wave (SDW) antiferromagnetism in pure Cr. The existence of an incommensurate spin-density wave results from Fermi-surface nesting, which changes with electron concentration as atoms of different valence are introduced into Cr. This gives rise for most impurities to a prototypical composition-temperature ($x-T$) magnetic phase diagram, which is described quite well by a model of nesting electron-hole octahedra and electron reservoir, with changes in the amplitude of the spin-density wave and its wave vector corresponding to the changes with impurity concentration of the Néel temperature. There are, however, numerous cases of idiosyncratic behavior in the $x-T$ phase diagram, some of which appear to correspond to unusual features in the pressure-temperature ($p-T$) phase diagram, e.g., in the CrFe, CrAl, and CrSi alloy systems. With these exceptions and a few others, the effect of impurities in the same group of the periodic table is fairly similar, so that this classification is used for the description of both the $x-T$ and $p-T$ phase diagrams. The properties of the alloy systems for each group of impurities are first summarized in the context of the $x-T$ phase diagram. The general features of the various physical properties are then considered: (1) magnetic susceptibility, whose temperature dependence signals the existence of local moments in some cases; (2) transport properties, in particular, electrical resistivity and thermopower, which show characteristic temperature dependence corresponding to the occurrence of spin fluctuations around the Néel temperature $T_N$, and in some cases well into the paramagnetic phase, followed below $T_N$ by effects due to the electron-hole condensation in the ordered AFM phase, and in some cases at lower temperatures to the formation of local impurity states; and (3) magnetoelastic properties, which show large effects associated with the spin-density wave and with SDW fluctuations in Cr alloys just as in pure Cr. Analysis of magnetic anomalies in the thermal expansion and bulk modulus in terms of magnetic Grüneisen parameters is employed for some Cr alloy systems to describe the large body of experimental data. The empirical correspondence between increasing volume and increasing electron concentration is illustrated for several systems. The study of dilute Cr alloys provides insight into the reason for pure Cr having a weak first-order Néel transition, and provides examples of other phase transitions, including the incommensurate-commensurate SDW, the spin-glass, and AFM-superconducting phase transitions. The similarities between the incommensurate SDW fluctuations in Cr and Cr alloys and in the high-temperature superconducting cuprates strongly motivates, in particular, the examination of the inelastic neutron-scattering results. Optical properties provide an interesting picture of the relation between the magnitude of the energy gap at the Fermi surface and the Néel temperature, which is quite different in the incommensurate and commensurate SDW alloys. Local probes providing microscopic information about the environment of an impurity are clearly of great potential value in Cr alloy systems. The Mössbauer effect has, however, yielded disappointingly little information, but other probes such as perturbed angular correlation and nuclear magnetic resonance have provided interesting results.

The energy balance of the elastodynamic field generated by a spherical cavity in a homogeneous, isotropic, and unbounded medium is studied. The near-field waves are found to play an essential role in the energy balance, transforming static energy into wave energy and vice versa, thus displaying a surprising ability to transmit wave energy in the direction opposite to wave propagation. The occurrence of such a negative wave energy clarifies the energy balance of sources, in which the waves are associated with energy dissipation rather than radiation.

Kolmogorov's refined similarity hypotheses are shown to hold true for a variety of stochastic processes besides high-Reynolds-number turbulent flows, for which they were originally proposed. In particular, just as hypothesized for turbulence, there exists a variable $V$ whose probability density function attains a universal form. Analytical expressions for the probability density function of $V$ are obtained for Brownian motion as well as for the general case of fractional Brownian motion—the latter under some mild assumptions justified a posteriori. The properties of $V$ for the case of antipersistent fractional Brownian motion with the Hurst exponent of $\frac{1}{3}$ are similar in many details to those of high-Reynolds-number turbulence in atmospheric boundary layers a few meters above the ground. The one conspicuous difference between turbulence and the antipersistent fractional Brownian motion is that the latter does not posses the required skewness. Broad implications of these results are discussed.

Over sixty years ago, it was suggested that there is a time associated with the passage of a particle under a tunneling barrier. The existence of such a time is now well accepted; in fact the time has been measured experimentally. There is no clear consensus, however, about the existence of a simple expression for this time, and the exact nature of that expression. The proposed expressions fall into three main classes. The authors argue that expressions based on following a feature of a wave packet through the barrier have little physical significance. A second class tries to identify a set of classical paths associated with the quantum-mechanical motion and then tries to average over these. This class is too diverse to permit assessment as a single entity. The third class invokes a physical clock involving degrees of freedom in addition to that involved in tunneling. This not only is a prescription for the derivation of expressions for the traversal time but also leads to a direct relationship to experiment.

The author reviews the status of our understanding of nucleosynthesis of the light nuclei ($Z<\mathrm{}6\mathrm{}$). The standard view today is that these elements are, for the most part, generated by two different processes: first, thermonuclear reactions in the early universe (big-bang nucleosynthesis or (BBN), and second, galactic cosmic-ray-induced spallation reactions (GCR) in cold interstellar atoms. A third contribution comes from stellar processes. The arguments in favor of this view are presented. Numerous astrophysical and cosmological implications are discussed, such as the baryonic density, the possible existence of baryonic dark matter and of nonbaryonic (exotic) matter, the constraints imposed on new particle physics, the leptonic number of the universe, the increase in cosmic entropy since primordial nucleosynthesis, and the constancy of the "constants" of physics.

The stability or lack thereof of nonrelativistic fermionic systems to interactions is studied within the renormalization-group (RG) framework, in close analogy with the study of critical phenomena using ${\phi }^4$ scalar field theory. A brief introduction to ${\phi }^4$ theory in four dimensions and the path-integral formulation for fermions is given before turning to the problem at hand. As for the latter, the following procedure is used. First, the modes on either side of the Fermi surface within a cutoff $\Lambda$ are chosen for study, in analogy with the modes near the origin in ${\phi }^4$ theory, and a path integral is written to describe them. Next, an RG transformation that eliminates a part of these modes, but preserves the action of the noninteracting system, is identified. Finally the possible perturbations of this free-field fixed point are classified as relevant, irrelevant or marginal. A $d=1\mathrm{}$ warmup calculation involving a system of fermions shows how, in contrast to mean-field theory, which predicts a charge-density wave for arbitrarily weak repulsion, and superconductivity for arbitrarily weak attraction, the renormalization-group approach correctly yields a scale-invariant system (Luttinger liquid) by taking into account both instabilities. Application of the renormalization group in $d=2\mathrm{} \mathrm{and} 3$, for rotationally invariant Fermi surfaces, automatically leads to Landau's Fermi-liquid theory, which appears as a fixed point characterized by an effective mass and a Landau function $F$, with the only relevant perturbations being of the superconducting (BCS) type. The functional flow equations for the BCS couplings are derived and separated into an infinite number of flows, one for each angular momentum. It is shown that similar results hold for rotationally noninvariant (but time-reversal-invariant) Fermi surfaces also, with obvious loss of rotational invariance in the parametrization of the fixed-point interactions. A study of a nested Fermi surface shows an additional relevant flow leading to charge-density-wave formation. It is pointed out that, for small $\frac{\Lambda }{K_F}$, a $\frac{1}{N}$ expansion emerges, with $N=\frac{K_F}{\Lambda }$, which explains why one is able to solve the narrow-cutoff theory. The search for non-Fermi liquids in $d=2\mathrm{}$ using the RG is discussed. Bringing a variety of phenomena (Landau theory, charge-density waves, BCS instability, nesting, etc.) under the one unifying principle of the RG not only allows us to better understand and unify them, but also paves the way for generalizations and extensions. The article is pedagogical in nature and is expected to be accessible to any serious graduate student. On the other hand, its survey of the vast literature is mostly limited to the RG approach.

Spin-density waves (SDWs) are broken-symmetry ground states of metals, the name referring to the periodic modulation of the spin density with period, ${\lambda }_0=\frac{\pi }{k_F}$, determined by the Fermi wave vector $k_F$. The state, originally postulated by Overhauser, has been found in several organic linear-chain compounds. The development of the SDW state opens up a gap in the single-particle excitation spectrum, and the ground state is close to that of an antiferromagnet, as shown by a wide range of magnetic studies. Because of the magnetic ground state and of the incommensurate periodic spin modulation (which can be thought of as two periodic charge modulations in the two spin subbands), both collective charge and spin excitations may occur. These couple to ac magnetic and electric fields, which leads to antiferromagnetic resonances and frequency-dependent collective-mode conductivity. Both have been observed in the spin-density-wave ground state. The interaction of the collective mode with impurities pins the mode to the underlying lattice, and therefore the collective-mode charge excitations occur at finite frequencies in the long-wavelength limit. The mode can also be induced to execute a translational motion upon the application of a dc field which exceeds the threshold field $E_T$. Many of the observations on the ac, and on the nonlinear dc, response are similar to those which occur in materials with a charge-density-wave ground state. At low temperatures a novel type of collective transport suggestive of a tunneling process is observed. These low-temperature phenomena remain unexplained.

Breaking of spatial homogeneity and the emergence of spatio-temporal order and disorder are striking phenomena abundant in nature. One possible origin for such ordering and disordering processes and for the transition between them is discussed.

In this paper, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed. Both macroscopically homogeneous and heterogeneous rocks are considered. The latter are characterized by large-scale spatial variations and correlations in their effective properties and include rocks that may be characterized by several distinct degrees of porosity, a well-known example of which is a fractured rock with two degrees of porosity—those of the pores and of the fractures. First, the diagenetic processes that give rise to the present reservoir rocks are discussed and a few geometrical models of such processes are described. Then, measurement and characterization of important properties, such as pore-size distribution, pore-space topology, and pore surface roughness, and morphological properties of fracture networks are discussed. It is shown that fractal and percolation concepts play important roles in the characterization of rocks, from the smallest length scale at the pore level to the largest length scales at the fracture and fault scales. Next, various structural models of homogeneous and heterogeneous rock are discussed, and theoretical and computer simulation approaches to flow, dispersion, and displacement in such systems are reviewed. Two different modeling approaches to these phenomena are compared. The first approach is based on the classical equations of transport supplemented with constitutive equations describing the transport and other important coefficients and parameters. These are called the continuum models. The second approach is based on network models of pore space and fractured rocks; it models the phenomena at the smallest scale, a pore or fracture, and then employs large-scale simulation and modern concepts of the statistical physics of disordered systems, such as scaling and universality, to obtain the macroscopic properties of the system. The fundamental roles of the interconnectivity of the rock and its wetting properties in dispersion and two-phase flows, and those of microscopic and macroscopic heterogeneities in miscible displacements are emphasized. Two important conceptual advances for modeling fractured rocks and studying flow phenomena in porous media are also discussed. The first, based on cellular automata, can in principle be used for computing macroscopic properties of flow phenomena in any porous medium, regardless of the complexity of its structure. The second, simulated annealing, borrowed from optimization processes and the statistical mechanics of spin glasses, is used for finding the optimum structure of a fractured reservoir that honors a limited amount of experimental data.

Chaotic time series data are observed routinely in experiments on physical systems and in observations in the field. The authors review developments in the extraction of information of physical importance from such measurements. They discuss methods for (1) separating the signal of physical interest from contamination ("noise reduction"), (2) constructing an appropriate state space or phase space for the data in which the full structure of the strange attractor associated with the chaotic observations is unfolded, (3) evaluating invariant properties of the dynamics such as dimensions, Lyapunov exponents, and topological characteristics, and (4) model making, local and global, for prediction and other goals. They briefly touch on the effects of linearly filtering data before analyzing it as a chaotic time series. Controlling chaotic physical systems and using them to synchronize and possibly communicate between source and receiver is considered. Finally, chaos in space-time systems, that is, the dynamics of fields, is briefly considered. While much is now known about the analysis of observed temporal chaos, spatio-temporal chaotic systems pose new challenges. The emphasis throughout the review is on the tools one now has for the realistic study of measured data in laboratory and field settings. It is the goal of this review to bring these tools into general use among physicists who study classical and semiclassical systems. Much of the progress in studying chaotic systems has rested on computational tools with some underlying rigorous mathematics. Heuristic and intuitive analysis tools guided by this mathematics and realizable on existing computers constitute the core of this review.

Irreversible random sequential adsorption (RSA) on lattices, and continuum "car parking" analogues, have long received attention as models for reactions on polymer chains, chemisorption on single-crystal surfaces, adsorption in colloidal systems, and solid state transformations. Cooperative generalizations of these models (CSA) are sometimes more appropriate, and can exhibit richer kinetics and spatial structure, e.g., autocatalysis and clustering. The distribution of filled or transformed sites in RSA and CSA is not described by an equilibrium Gibbs measure. This is the case even for the saturation "jammed" state of models where the lattice or space cannot fill completely. However exact analysis is often possible in one dimension, and a variety of powerful analytic methods have been developed for higher dimensional models. Here we review the detailed understanding of asymptotic kinetics, spatial correlations, percolative structure, etc., which is emerging for these far-from-equilibrium processes.

Radar is a powerful technique that has furnished otherwise unavailable information about solar system bodies for three decades. The advantages of radar in planetary astronomy result from (1) the observer's control of all the attributes of the coherent signal used to illuminate the target, especially the wave form's time/frequency modulation and polarization; (2) the ability of radar to resolve objects spatially via measurements of the distribution of echo power in time delay and Doppler frequency; (3) the pronounced degree to which delay-Doppler measurements constrain orbits and spin vectors; and (4) centimeter-to-meter wavelengths, which easily penetrate optically opaque planetary clouds and cometary comae, permit investigation of near-surface macrostructure and bulk density, and are sensitive to high concentrations of metal or, in certain situations, ice. Planetary radar astronomy has primarily involved observations with Earth-based radar telescopes, but also includes some experiments with a spaceborne transmitter or receiver. In addition to providing a wealth of information about the geological and dynamical properties of asteroids, comets, the inner planets, and natural satellites, radar experiments have established the scale of the solar system, have contributed significantly to the accuracy of planetary ephemerides, and have helped to constrain theories of gravitation. This review outlines radar astronomical techniques and describes principal observational results.

It is becoming increasingly clear that the concept of a diquark (a two-quark system) is important for understanding hadron structure and high-energy particle reactions. According to our present knowledge of quantum chromodynamics (QCD), diquark correlations arise in part from spin-dependent interactions between two quarks, from quark radial or orbital excitations, and from quark mass differences. Diquark substructures affect the static properties of baryons and the mechanisms of baryon decay. Diquarks also play a role in hadron production in hadron-initiated reactions, deep-inelastic lepton scattering by hadrons, and in $e^{+}{e}^{-}$ reactions. Diquarks are important in the formation and properties of baryonium and mesonlike semistable states. Many spin effects observed in high-energy exclusive reactions pose severe problems for the pure quark picture of baryons and might be explained by the introduction of diquarks as hadronic constituents. There is considerable controversy, not about the existence of diquarks in hadrons, but about their properties and their effects. In this work a broad selection of the main ideas about diquarks is reviewed.

This article reviews the current situation in the field of rare $K$ decays: the relevant phenomenology, the present experimental situation, and prospects for the near future. Study of rare $K$ decays can make a significant contribution in a number of different frontier areas of research in high-energy physics. In the area of $\mathrm{CP}$ violation, study of such rare decays as $K_L^0\to {\pi }^0{e}^{+}{e}^{-}$, $K_L^0\to {\pi }^0{\mu }^{+}{\mu }^{-}$, $K_L^0\to {\pi }^0\nu \overline{\nu }$, and muon polarization in $K_L^0\to {\mu }^{+}{\mu }^{-}$ can provide important complementary information to what has been learned from the decay $K_L^0\to \pi \pi$. Even though experiments with sufficient accuracy to make a meaningful study of $\mathrm{CP}$ violation are still a few years away, significant progress has been made in this general area during the last decade. A second major area of interest in the field of rare $K$ decays is the search for processes forbidden in the Standard Model, e.g., $K_L^0\to \mu e$ and $K^{+}\to {\pi }^{+}{\mu }^{+}{e}^{-}$. Various extensions of the Standard Model predict that these processes will occur with branching fractions in the range of ${10}^{-10\mathrm{}}$ to ${10}^{-15\mathrm{}}$. Experiments of the last decade have pushed the limits into the ${10}^{-10\mathrm{}}$ to ${10}^{-11\mathrm{}}$ range, and further improvements in sensitivity of one to two orders of magnitude can be expected in the next few years. $K$ decays allow one also to study higher-order weak-interaction processes such as $K_L^0\to {\mu }^{+}{\mu }^{-}$, $K_L^0\to e^{+}{e}^{-}$, $K^{+}\to {\pi }^{+}\nu \overline{\nu }$, which are forbidden to first order in the Standard Model. Because of strong suppression, these decay modes offer potential windows on new physics; in addition, they may offer the most reliable measurement of $V_{\mathrm{td}}$, one of the elements of the weak mixing matrix in the quark sector. The studies of the ${\mu }^{+}{\mu }^{-}$ channel have achieved data samples of close to 1000 events; the other two modes should be observed for the first time in the next few years. Finally, as a byproduct of these studies, one has been able to look simultaneously for new light particles into which the $K$ meson could decay. Limits obtained for various hypothetical particles are summarized.