The terms glass'' and liquid'' are defined in a dynamic sense, with a sublinear response [rho]=[partial derivative][ital E]/[partial derivative][ital j][vert bar][sub [ital j][r arrow]0] characterizing the truly superconducting vortex glass and a finite resistivity [rho]([ital j][r arrow]0)[gt]0 being the signature of the liquid phase. The smallness of [ital j][sub [ital c]]/[ital j][sub o] allows one to discuss the influence of quenched disorder in terms of the weak collective pinning theory. Supplementing the traditional theory of weak collective pinning to take into account thermal and quantum fluctuations, as well as the new scaling concepts for elastic media subject to a random potential, this modern version of the weak collective pinning theory consistently accounts for a large number of novel phenomena, such as the broad resistive transition, thermally assisted flux flow, giant and quantum creep, and the glassiness of the solid state. The strong layering of the oxides introduces additional new features into the thermodynamic phase diagram, such as a layer decoupling transition, and modifies the mechanism of pinning and creep in various ways. The presence of strong (correlated) disorder in the form of twin boundaries or columnar defects not only is technologically relevant but also provides the framework for the physical realization of novel thermodynamic phases such as the Bose glass. On a macroscopic scale the vortex system exhibits self-organized criticality, with both the spatial and the temporal scale accessible to experimental investigations.

Theoretical ideas and experimental results concerning high-temperature superconductors are reviewed. Special emphasis is given to calculations performed with the help of computers applied to models of strongly correlated electrons proposed to describe the two-dimensional CuO2 planes. The review also includes results using several analytical techniques. The one- and three-band Hubbard models and the t-J model are discussed, and their behavior compared against experiments when available. The author found, among the conclusions of the review, that some experimentally observed unusual properties of the cuprates have a natural explanation through Hubbard-like models. In particular, abnormal features like the mid-infrared band of the optical conductivity sigma(omega), the new states observed in the gap in photoemission experiments, the behavior of the spin correlations with doping, and the presence of phase separation in the copper oxide superconductors may be explained, at least in part, by these models. Finally, the existence of superconductivity in Hubbard-like models is analyzed. Some aspects of the recently proposed ideas to describe the cuprates as having a d(x2-y2) superconducting condensate at low temperatures are discussed. Numerical results favor this scenario over others. It is concluded that computational techniques provide a useful, unbiased tool for studying the difficult regime where electrons are strongly interacting, and that considerable progress can be achieved by comparing numerical results against analytical predictions for the properties of these models. Future directions of the active field of computational studies of correlated electrons are briefly discussed.

The macroscopic electric polarization of a crystal is often defined as the dipole of a unit cell. In fact, such a dipole moment is ill defined, and the above definition is incorrect. Looking more closely, the quantity generally measured is differential polarization, defined with respect to a ''reference state'' of the same material. Such differential polarizations include either derivatives of the polarization (dielectric permittivity, Born effective charges, piezoelectricity, pyroelectricity) or finite differences (ferroelectricity). On the theoretical side, the differential concept is basic as well. Owing to continuity, a polarization difference is equivalent to a macroscopic current, which is directly accessible to the theory as a bulk property. Polarization is a quantum phenomenon and cannot be treated with a classical model, particularly whenever delocalized valence electrons are present in the dielectric. In a quantum picture, the current is basically a property of the phase of the wave functions, as opposed to the charge, which is a property of their modulus. An elegant and complete theory has recently been developed by King-Smith and Vanderbilt, in which the polarization difference between any two crystal states-in a null electric field-takes the form of a geometric quantum phase. The author gives a comprehensive account of this theory, which is relevant for dealing with transverse-optic phonons, piezoelectricity, and ferroelectricity. Its relation to the established concepts of linear-response theory is also discussed. Within the geometric phase approach, the relevant polarization difference occurs as the circuit integral of a Berry connection (or ''vector potential''), while the corresponding curvature (or ''magnetic field'') provides the macroscopic linear response.

Various experimental methods based on positron annihilation have evolved into important tools for researching the structure and properties of condensed matter. In particular, positron techniques are useful for the investigation of defects in solids and for the investigation of solid surfaces. Experimental methods need a comprehensive theory for a deep, quantitative understanding of the results. In the case of positron annihilation, the relevant theory includes models needed to describe the positron states as well as the different interaction processes in matter. In this review the present status of the theory of positrons in solids and on solid surfaces is given. The review consists of three main parts describing (a) the interaction processes, (b) the theory and methods for calculating positron states, and (c) selected recent results of positron studies of condensed matter.

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 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 phi4 scalar field theory. A brief introduction to phi4 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 A are chosen for study, in analogy with the modes near the origin in phi4 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 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 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 LAMBDA/K(F), a 1/N expansion emerges, with N = K(F)/LAMBDA, which explains why one is able to solve the narrow-cutoff theory. The search for non-Fermi liquids in d = 2 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.

Over six 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.

During the past five years, major progress has been made in the experimental study of solid hydrogen at ultrahigh pressures as a result of developments in diamond-cell technology. Pressures at which metallization has been predicted to occur have been reached (250-300 Gigapascals). Detailed studies of the dynamic, structural, and electronic properties of dense hydrogen reveal a system unexpectedly rich in physical phenomena, exhibiting a variety of transitions at ultrahigh pressures. This colloquium explores the study of dense hydrogen as an archetypal problem in condensed-matter physics.

The reliable development of highly complex organisms is an intriguing and fascinating problem. The genetic material is, as a rule, the same in each cell of an organism. How then do cells, under the influence of their common genes, produce spatial patterns Simple models are discussed that describe the generation of patterns out of an initially nearly homogeneous state. They are based on nonlinear interactions of at least two chemicals and on their diffusion. The concepts of local autocatalysis and of long-range inhibition play a fundamental role. Numerical simulations show that the models account for many basic biological observations such as the regeneration of a pattern after excision of tissue or the production of regular (or nearly regular) arrays of organs during (or after) completion of growth. Very complex patterns can be generated in a reproducible way by hierarchical coupling of several such elementary reactions. Applications to animal coats and to the generation of polygonally shaped patterns are provided. It is further shown how to generate a strictly periodic pattern of units that themselves exhibit a complex and polar fine structure. This is illustrated by two examples: the assembly of photoreceptor cells in the eye of [ital Drosophila] and the positioning of leaves and axillary buds in a growing shoot. In both cases, the substructures have to achieve an internal polarity under the influence of some primary pattern-forming system existing in the fly's eye or in the plant. The fact that similar models can describe essential steps in organisms as distantly related as animals and plants suggests that they reveal some universal mechanisms.

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 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 Neel 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 Neel 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 Gruneisen 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 Neel 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 Neel 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 Mossbauer effect has, however, yielded disappointingly little information, but other probes such as perturbed angular correlation and nuclear magnetic resonance have provided interesting results.

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(WB) = (pi/ln 2) square-root 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(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.

An overview is presented of methods for time-dependent treatments of molecules as systems of electrons and nuclei. The theoretical details of these methods are reviewed and contrasted in the light of a recently developed time-dependent method called electron-nuclear dynamics. Electron-nuclear dynamics (END) is a formulation of the complete dynamics of electrons and nuclei of a molecular system that eliminates the necessity of constructing potential-energy surfaces. Because of its general formulation, it encompasses many aspects found in other formulations and can serve as a didactic device for clarifying many of the principles and approximations relevant in time-dependent treatments of molecular systems. The END equations are derived from the time-dependent variational principle applied to a chosen family of efficiently parametrized approximate state vectors. A detailed analysis of the END equations is given for the case of a single-determinantal state for the electrons and a classical treatment of the nuclei. The approach leads to a simple formulation of the fully nonlinear time-dependent Hartree-Fock theory including nuclear dynamics. The nonlinear END equations with the ab initio Coulomb Hamiltonian have been implemented at this level of theory in a computer program, ENDyne, and have been shown feasible for the study of small molecular systems. Implementation of the Austin Model 1 semiempirical Hamiltonian is discussed as a route to large molecular systems. The linearized END equations at this level of theory are shown to lead to the random-phase approximation for the coupled system of electrons and nuclei. The qualitative features of the general nonlinear solution are analyzed using the results of the linearized equations as a first approximation. Some specific applications of END are presented, and the comparison with experiment and other theoretical approaches is discussed.

Momentum-conserving lattice gases are simple, discrete, microscopic models of fluids. This review describes their hydrodynamics, with particular attention given to the derivation of macroscopic constitutive equations from microscopic dynamics. Lattice-gas models of phase separation receive special emphasis. The current understanding of phase transitions in these momentum-conserving models is reviewed; included in this discussion is a summary of the dynamical properties of interfaces. Because the phase-separation models are microscopically time irreversible, interesting questions are raised about their relationship to real fluid mixtures. Simulation of certain complex-fluid problems, such as multiphase flow through porous media and the interaction of phase transitions with hydrodynamics, is illustrated.

Most of our knowledge of the electronic structure of atoms and molecules is derived from excitation energies and transition probabilities. These observable quantities are related to the electronic wave functions by integrals over unmeasured variables. Another observable more directly related to the wave function than energy or transition probability is the single-electron momentum density, the probability that an electron in a well-defined orbital has a given value of momentum. Over the last twenty years a technique has been developed for measuring momentum densities in atoms and molecules. The technique, (e,2e) spectroscopy, is based on electron-impact ionization with complete determination of the momentum of both incoming and outgoing electrons. The conditions necessary to extract momentum-density information from the ionization experiments are examined and related to general theories of electron scattering. Different experimental arrangements are reviewed and momentum-density results from selected examples are discussed.

Spin-density waves (SDWs) are broken-symmetry ground states of metals, the name referring to the periodic modulation of the spin density with period, lambda0=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.

The authors present an overview of ongoing studies of the rich dynamical behavior of the uniform, deterministic Burridge-Knopoff model of an earthquake fault, discussing the model's behavior in the context of current seismology. The topics considered include: (1) basic properties of the model, such as the distinction between small and large events and the magnitude vs frequency distribution; (2) dynamics of individual events, including dynamical selection of rupture propagation speeds; (3) generalizations of the model to more realistic, higher-dimensional models; and (4) studies of predictability, in which artificial catalogs generated by the model are used to test and determine the limitations of pattern recognition algorithms used in seismology.

Halo states extend over an unusually large space where many of their properties hinge on the tail of the wave functions. Their levels lie mainly just below the thresholds for neutron-emission channels. This short review covers the main distinguishing features of halos and how they are revealed in experiments. Special emphasis is placed on the large variety of experiments apt to study halo structures. Some aspects of current research are treated in greater detail.