Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy Σ and the electron-hole interaction. A good approximation for Σ is obtained with Hedin's $\mathrm{GW}$ approach, using density-functional theory as a zero-order solution. First-principles $\mathrm{GW}$ calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of Σ. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

The present “state of the art” and the path to future progress in high-spatial-resolution imaging interferometry is reviewed. The review begins with a treatment of the fundamentals of stellar optical interferometry, the origin, properties, and optical effects of turbulence in the Earth’s atmosphere, the passive methods such as speckle interferometry that are applied on a single telescope to overcome atmospheric image degradation, and various other techniques. These topics include differential speckle interferometry, speckle spectroscopy and polarimetry, phase diversity, wave-front shearing interferometry, phase-closure methods, dark speckle imaging, as well as the limitations imposed by the detectors on the performance of speckle imaging. A brief account is given of the technological innovation of adaptive optics to compensate for atmospheric effects on the image in real time. A major advancement involves the transition from single-aperture to dilute-aperture interferometry using multiple telescopes. Therefore the review deals with recent developments involving ground-based and space-based optical arrays. Emphasis is placed on the problems specific to delay lines, beam recombination, polarization, dispersion, fringe tracking, bootstrapping, coherencing and cophasing, and recovery of the visibility functions. The role of adaptive optics in enhancing visibilities is also discussed. The applications of interferometry, such as imaging, astrometry, and nulling, are described. The mathematical intricacies of the various “postdetection” image-processing techniques are examined critically. The review concludes with a discussion of the astrophysical importance and the prospects of interferometry.

Since the first days of high-$T_{\mathrm{c}}$ superconductivity, the materials science and the physics of grain boundaries in superconducting compounds have developed into fascinating fields of research. Unique electronic properties, different from those of the grain boundaries in conventional metallic superconductors, have made grain boundaries formed by high-$T_{\mathrm{c}}$ cuprates important tools for basic science. They are moreover a key issue for electronic and large-scale applications of high-$T_{\mathrm{c}}$ superconductivity. The aim of this review is to give a summary of this broad and dynamic field. Starting with an introduction to grain boundaries and a discussion of the techniques established to prepare them individually and in a well-defined manner, the authors present their structure and transport properties. These provide the basis for a survey of the theoretical models developed to describe grain-boundary behavior. Following these discussions, the enormous impact of grain boundaries on fundamental studies is reviewed, as well as high-power and electronic device applications.

Single-bubble sonoluminescence occurs when an acoustically trapped and periodically driven gas bubble collapses so strongly that the energy focusing at collapse leads to light emission. Detailed experiments have demonstrated the unique properties of this system: the spectrum of the emitted light tends to peak in the ultraviolet and depends strongly on the type of gas dissolved in the liquid; small amounts of trace noble gases or other impurities can dramatically change the amount of light emission, which is also affected by small changes in other operating parameters (mainly forcing pressure, dissolved gas concentration, and liquid temperature). This article reviews experimental and theoretical efforts to understand this phenomenon. The currently available information favors a description of sonoluminescence caused by adiabatic heating of the bubble at collapse, leading to partial ionization of the gas inside the bubble and to thermal emission such as bremsstrahlung. After a brief historical review, the authors survey the major areas of research: Section II describes the classical theory of bubble dynamics, as developed by Rayleigh, Plesset, Prosperetti, and others, while Sec. III describes research on the gas dynamics inside the bubble. Shock waves inside the bubble do not seem to play a prominent role in the process. Section IV discusses the hydrodynamic and chemical stability of the bubble. Stable single-bubble sonoluminescence requires that the bubble be shape stable and diffusively stable, and, together with an energy focusing condition, this fixes the parameter space where light emission occurs. Section V describes experiments and models addressing the origin of the light emission. The final section presents an overview of what is known, and outlines some directions for future research.

Quantum theory has found a new field of application in the realm of information and computation during recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some notable aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as examples of the impact of quanta on the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement made possible in information processing by a quantum computer. Finally the authors provide some examples of current experimental realizations for quantum computers and future prospects.

The authors review recent advances in the physics of strongly interacting charged systems functioning in water at room temperature. In these systems, many phenomena go beyond the framework of mean-field theories, whether linear Debye-Hückel or nonlinear Poisson-Boltzmann, culminating in charge inversion—a counterintuitive phenomenon in which a strongly charged particle, called a macroion, binds so many counterions that its net charge changes sign. The review discusses the universal theory of charge inversion based on the idea of a strongly correlated liquid of adsorbed counterions, similar to a Wigner crystal. This theory has a vast array of applications, particularly in biology and chemistry; for example, in the presence of positive multivalent ions (e.g., polycations), the DNA double helix acquires a net positive charge and drifts as a positive particle in an electric field. This simplifies DNA uptake by the cell as needed for gene therapy, because the cell membrane is negatively charged. Analogies of charge inversion to other fields of physics are also discussed.

The status of neutrino oscillation searches employing nuclear reactors as sources is reviewed. This technique, a direct continuation of the experiments that proved the existence of neutrinos, is today an essential tool in investigating the indications of oscillations found in studying neutrinos produced in the sun and in the earth’s atmosphere. The low energy of the reactor ${\overline{\nu }}_e$ makes them ideal for exploring oscillations with small mass differences and relatively large mixing angles. In the last several years the determination of the reactor antineutrino flux and spectrum has reached a high degree of accuracy. Hence measurements of these quantities at a given distance $L$ can be readily compared with the expectation at $L=0,$ thus testing the disappearance of ${\overline{\nu }}_e.$ Two recent experiments, CHOOZ and PALO VERDE, with baselines of about 1 km and sensitive to the neutrino mass differences associated with the atmospheric neutrino anomaly have collected data and published results recently. An ambitious project with a baseline of more than 100 km, KAMLAND, has now began to take data. This last reactor experiment will have a sensitivity sufficient to explore part of the oscillation phase space relevant to solar neutrino scenarios. It is the only envisioned experiment with a terrestrial source of neutrinos capable of addressing the solar neutrino puzzle.

The heavy-fermion compound ${\mathrm{UPt}}_3$ is the first compelling example of a superconductor with an order parameter of unconventional symmetry. To this day, it is the only unambiguous case of multiple superconducting phases. Twenty years of experiment and theory on the superconductivity of ${\mathrm{UPt}}_3$ are reviewed, with the aim of accounting for the multicomponent phase diagram and identifying the superconducting phases. First, the state above the superconducting critical temperature at $T_c=0.5\mathrm{}\mathrm{K}$ is briefly described: de Haas–van Alphen and other measurements demonstrate that this state is a Fermi liquid, with degeneracy fully achieved at $T_c.$ This implies that the usual BCS theory of superconductivity should hold, although the strong magnetic interactions suggest the possibility of an unconventional superconducting order parameter. The role of the weak antiferromagnetic order below $T_N=5\mathrm{}\mathrm{K}$ in causing phase multiplicity is examined. A comprehensive analysis of which superconducting states are possible is given, and the theoretical basis for each of the main candidates is considered. The behavior of various properties at low temperature $(T\ll T_c)$ is reviewed. The experiments clearly indicate the presence of nodes in the superconducting gap function of all three phases. In particular, the low-temperature low-field phase has a gap with a line node in the basal plane and point nodes along the hexagonal $c$ axis. The phase diagram in the magnetic-field–temperature plane has been determined in detail by ultrasound and thermodynamic measurements. Experiments under pressure indicate a coupling between antiferromagnetism and superconductivity and provide additional clues about the order parameter. Theoretically, Ginzburg-Landau theory is the tool that elucidates the phase diagram, while calculations of the temperature and field dependence of physical quantities have been used to compare different order parameters to experiment. On balance, the data point to a two-component order parameter belonging to either the $E_{1g}$ or the $E_{2u}$ representation, with degeneracy lifted by a coupling to the symmetry-breaking magnetic order. However, no single theoretical scenario is completely consistent with all the data. The coupling of superconductivity and magnetism may be the weakest link in the current picture of ${\mathrm{UPt}}_3,$ and full understanding depends on the resolution of this issue.

Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they are in fact intimately related. In this review the author shows how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission. The derivation of many key results differentiates this review from the usual presentation in that they are shown to follow logically from one crucial property of relative entropy. Within the review, optimal bounds on the enhanced speed that quantum computers can achieve over their classical counterparts are outlined using information-theoretic arguments. In addition, important implications of quantum information theory for thermodynamics and quantum measurement are intermittently discussed. A number of simple examples and derivations, including quantum superdense coding, quantum teleportation, and Deutsch’s and Grover’s algorithms, are also included.

Quantum cryptography could well be the first application of quantum mechanics at the single-quantum level. The rapid progress in both theory and experiment in recent years is reviewed, with emphasis on open questions and technological issues.

The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to second-order phase transitions, from superconductivity, superfluidity, and Bose-Einstein condensation to liquid crystals and strings in field theory. The authors give an overview of various phenomena described by the complex Ginzburg-Landau equation in one, two, and three dimensions from the point of view of condensed-matter physicists. Their aim is to study the relevant solutions in order to gain insight into nonequilibrium phenomena in spatially extended systems.

Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.

A long-standing limitation of first-principles calculations of substitutional alloy phase diagrams is the difficulty in accounting for lattice vibrations. A survey of the theoretical and experimental literature seeking to quantify the effect of lattice vibrations on phase stability indicates that they can be significant. Typical vibrational entropy differences between phases are of the order of 0.1 to ${0.2k}_B/\mathrm{atom},$ which is comparable to the typical values of configurational entropy differences in binary alloys (at most ${0.693k}_B/\mathrm{atom}).\mathrm{}$ This article presents the basic formalism underlying ab initio phase diagram calculations, along with the generalization required to account for lattice vibrations. The authors review the various techniques allowing the theoretical calculation and the experimental determination of phonon dispersion curves and related thermodynamic quantities, such as vibrational entropy or free energy. A clear picture of the origin of vibrational entropy differences between phases in an alloy system is presented that goes beyond the traditional bond counting and volume change arguments. Vibrational entropy change can be attributed to the changes in chemical bond stiffness associated with the changes in bond length that take place during a phase transformation. This so-called “bond stiffness vs bond length” interpretation both summarizes the key phenomenon driving vibrational entropy changes and provides a practical tool to model them.

This colloquium discusses the atomic structure of carbon nanotubes as deduced from high-resolution electron microscopy and electron diffraction in transmission through a single nanotube. The principal features of the observed micrographs are interpreted in terms of the cylindrical, chiral geometry of the atomic distribution of single-wall or multiwall nanotubes. In order to better understand the mechanism of image formation in electron diffraction, the authors propose optical simulation experiments using a laser pointer and a little “diffraction laboratory on a slide.” The simulations visibly reproduce all the features of the observed electron micrographs, namely, the quasihexagonal patterns of Bragg spots, the streaked nature of the spots, the doubling of the spot number induced by chirality, etc. The present colloquium should allow a general readership to appreciate the continuing efficiency and power of diffraction methods for the determination of the structure of macromolecules.

Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by “phantom traffic jams” even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems “freeze by heating”? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

This article reviews the current knowledge and understanding of the interstellar medium of our galaxy. The author first presents each of the three basic constituents—ordinary matter, cosmic rays, and magnetic fields—of the interstellar medium, with emphasis on their physical and chemical properties as inferred from a broad range of observations. The interaction of these interstellar constituents, both with each other and with stars, is then discussed in the framework of the general galactic ecosystem.

This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level.

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e., to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in nonequilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.

The theory of pure type-II superconductors at high magnetic fields and low temperatures has recently attracted much attention due to the discovery of de Haas–van Alphen oscillations deep in the vortex state. In this article the authors review the state of the art in this rapidly growing new field of research. The very existence of quantum magnetic oscillations deep in the vortex state poses challenging questions to the theorists working in this field. For a conventional extreme type-II superconductor in magnetic fields just below the upper critical field $H_{c2\mathrm{}},$ the quasiparticle spectrum is gapless and the de Haas–van Alphen effect is suppressed with respect to the corresponding normal-state signal due to superconducting induced currents near the vortex cores, which are of paramagnetic nature. Numerical simulations of the quasiparticle band structure in the Abrikosov vortex lattice show the existence of well-separated Landau bands below $H_{c2\mathrm{}}.$ An analytical perturbative approach, which emphasizes the importance of phase coherence in quasiparticle scattering by the pair potential in the Abrikosov lattice, predicts a relatively weak magnetic breakdown of the corresponding cyclotron orbits. In contrast to the situation in the Abrikosov lattice state, a theory based on a random vortex lattice model yields large exponential decay of the de Haas–van Alphen oscillations with the superconducting order parameter below $H_{c2\mathrm{}}.$ The disordered nature of the vortex state near $H_{c2\mathrm{}}$ in real superconductors, where long-range phase coherence in the superconducting order parameter is destroyed, could explain the success of this model in interpreting experimental data below $H_{c2\mathrm{}}.$ In the Abrikosov vortex lattice state, which usually stabilizes well below $H_{c2\mathrm{}},$ the residual damping of the de Haas–van Alphen amplitude is significantly reduced. In quasi-two-dimensional superconductors, phase fluctuations associated with sliding Bragg chains along principal axes in the vortex lattice lead to a weak first-order melting transition far below the mean-field $H_{c2\mathrm{}}.$ Superconducting fluctuations dominate the additional damping of the de Haas–van Alphen oscillations in this vortex liquid state. Below the first-order freezing point, this damping is predicted to weaken signifiFantly.

An overview is presented of the various phases predicted to occur when gases are absorbed within a bundle of carbon nanotubes. The behavior may be characterized by an effective dimensionality, which depends on the species and the temperature. Small molecules are strongly attracted to the interstitial channels between tubes. There, they undergo transitions between ordered and disordered quasi-one-dimensional (1D) phases. Both small and large molecules display 1D and/or 2D phase behavior when adsorbed within the nanotubes, depending on the species and thermodynamic conditions. Finally, molecules adsorbed on the external surface of the bundle exhibit 1D behavior (striped phases), which crosses over to 2D behavior (monolayer film) and eventually 3D behavior (thick film) as the coverage is increased. The various phases exhibit a wide variety of thermal and other properties.