Resonant inelastic x-ray scattering (RIXS) has recently been a subject of remarkable progress due to the advent of high-brilliance synchrotron radiation sources. The authors present a review of both experimental and theoretical investigations of electrons in solids using this second-order optical process, in which there is coherent absorption and emission of x rays at resonance with electronic excitations. The review starts with some of the fundamental aspects of RIXS, after which are presented typical experimental data and their theoretical interpretation for various materials. The first class of materials considered is semiconductors and insulators (Si, C, and BN), which are typical systems with weak electron correlation, and the data are interpreted based on electronic states described by an energy-band model. Effects of symmetry of electronic states and electron momentum conservation are discussed. At the opposite extreme are rare-earth systems (metals and oxides), in which the $4f$ electrons are almost localized with strong electron correlation. The observations are interpreted based on the effects of intra-atomic multiplet coupling and weak interatomic electron transfer, which are well described with an Anderson impurity model or a cluster model. In this context a narrowing of spectral width in the excitation spectrum, polarization dependence, and the magnetic circular dichroism in ferromagnetic materials are discussed. The authors then consider transition-metal compounds, materials with electron correlation strengths intermediate between semiconductors and rare-earth systems. In these interesting cases there is an interplay of intra-atomic and interatomic electronic interactions that leads to limitations of both the band model and the Anderson impurity model. Finally, other topics in resonant x-ray emission studies of solids are described briefly.

This article reviews the current theoretical and experimental status of the field of muon decay and its potential to search for new physics beyond the standard model. The importance of rare muon processes with lepton flavor violation is highly stressed, together with precision measurements of normal muon decay. Recent up-to-date motivations of lepton flavor violation based on supersymmetric models, in particular supersymmetric grand unified theories, are described along with other theoretical models. Future prospects of experiments and muon sources of high intensity for further progress in this field are also discussed.

This article is a pedagogical exploration of the nonperturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry. After briefly reviewing the importance of chiral symmetry in particle physics, the author discusses how anomalies complicate lattice formulations. Considerable information can be deduced from effective chiral Lagrangians, helping interpret the expectations for lattice models and elucidating the role of the CP-violating parameter Θ. One particularly elegant scheme for exploring this physics on the lattice is presented in some detail. This uses an auxiliary extra space-time dimension, with the physical world being a four-dimensional interface.

Atmospheric neutrinos are produced as decay products in hadronic showers resulting from collisions of cosmic rays with nuclei in the atmosphere. Electron neutrinos and muon neutrinos are produced mainly by the decay chain of charged pions to muons to electrons. Atmospheric neutrinos have been observed by large underground detectors. Depending on their energy, these neutrinos are observed as fully contained events, partially contained events, or upward going muon events. The energy range covered by these events is from a few hundred MeV to above 100 GeV. It has been known for about ten years that some data suggested the existence of neutrino oscillations. With the recent increase in event data, especially from Super-Kamiokande, it is concluded that the atmospheric neutrino data give evidence for neutrino oscillations. Two-flavor ${\nu }_{\mu }\to {\nu }_{\tau }$ oscillations, with ${\sin }^{2}2\theta >0.88\mathrm{}$ and $\Delta m^2$ in the region of $2\times {10}^{-3}$ to $5\times {10}^{-3}{\mathrm{eV}}^2,$ explain all these data.

This article describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems. These stochastic wave-function-based approaches provide a very direct treatment of quantum many-body effects and serve as benchmarks against which other techniques may be compared. They complement the less demanding density-functional approach by providing more accurate results and a deeper understanding of the physics of electronic correlation in real materials. The algorithms are intrinsically parallel, and currently available high-performance computers allow applications to systems containing a thousand or more electrons. With these tools one can study complicated problems such as the properties of surfaces and defects, while including electron correlation effects with high precision. The authors provide a pedagogical overview of the techniques and describe a selection of applications to ground and excited states of solids and clusters.

This article gives an overview of recent x-ray diffraction experiments with time resolutions down to ${10}^{-13}\mathrm{s}.$ The scientific motivation behind the development is outlined, using examples from solid state physics and biology. The ultrafast resolution may be provided either by fast detectors or short x-ray pulses, and the limitations of both techniques are discussed on the basis of state of the art experiments. In particular, it is shown that with present designs, high time resolution reduces the structural information attainable with high spatial resolution, thereby limiting feasible experiments on the ultrashort time-scale. The first experiment showing subpicosecond conformation changes was recently achieved with simple solids using an ultrafast laser-produced plasma x-ray source. The principles of this experiment are described in detail.

We review a striking array of recent experiments and their theoretical interpretations on the superfluid transition in ${}^4\mathrm{He}$ in the presence of a heat flux $Q.\mathrm{}$ We define and evaluate a new set of critical point exponents. The statics and dynamics of the superfluid-normal interface are discussed, with special attention to the role of gravity. If $Q$ is in the same direction as gravity, a self-organized state can arise, in which the entire sample has a uniform reduced temperature, on either the normal or superfluid side of the transition. Finally, we review recent theory and experiment regarding the heat capacity at constant $Q.\mathrm{}$ The excitement that surrounds this field arises from the fact that advanced thermometry and the future availability of a microgravity experimental platform aboard the International Space Station will soon open to experimental exploration decades of reduced temperature that were previously inaccessible.

Pairing symmetry in the cuprate superconductors is an important and controversial topic. The recent development of phase-sensitive tests, combined with the refinement of several other symmetry-sensitive techniques, has for the most part settled this controversy in favor of predominantly $d$-wave symmetry for a number of optimally hole- and electron-doped cuprates. This paper begins by reviewing the concepts of the order parameter, symmetry breaking, and symmetry classification in the context of the cuprates. After a brief survey of some of the key non-phase-sensitive tests of pairing symmetry, the authors extensively review the phase-sensitive methods, which use the half-integer flux-quantum effect as an unambiguous signature for $d$-wave pairing symmetry. A number of related symmetry-sensitive experiments are described. The paper concludes with a brief discussion of the implications, both fundamental and applied, of the predominantly $d$-wave pairing symmetry in the cuprates.

A quantum dot is a sub-micron-scale conducting device containing up to several thousand electrons. Transport through a quantum dot at low temperatures is a quantum-coherent process. This review focuses on dots in which the electron’s dynamics are chaotic or diffusive, giving rise to statistical properties that reflect the interplay between one-body chaos, quantum interference, and electron-electron interactions. The conductance through such dots displays mesoscopic fluctuations as a function of gate voltage, magnetic field, and shape deformation. The techniques used to describe these fluctuations include semiclassical methods, random-matrix theory, and the supersymmetric nonlinear σ model. In open dots, the approximation of noninteracting quasiparticles is justified, and electron-electron interactions contribute indirectly through their effect on the dephasing time at finite temperature. In almost-closed dots, where conductance occurs by tunneling, the charge on the dot is quantized, and electron-electron interactions play an important role. Transport is dominated by Coulomb blockade, leading to peaks in the conductance that at low temperatures provide information on the dot’s ground-state properties. Several statistical signatures of electron-electron interactions have been identified, most notably in the dot’s addition spectrum. The dot’s spin, determined partly by exchange interactions, can also influence the fluctuation properties of the conductance. Other mesoscopic phenomena in quantum dots that are affected by the charging energy include the fluctuations of the cotunneling conductance and mesoscopic Coulomb blockade.

Some properties of the world are fixed by physics derived from mathematical symmetries, while others are selected from an ensemble of possibilities. Several successes and failures of “anthropic” reasoning in this context are reviewed in light of recent developments in astrobiology, cosmology, and unification physics. Specific issues raised include our space-time location (including the reason for the present age of the universe), the time scale of biological evolution, the tuning of global cosmological parameters, and the origin of the Large Numbers of astrophysics and the parameters of the standard model. Out of the 20 parameters of the standard model, the basic behavior and structures of the world (nucleons, nuclei, atoms, molecules, planets, stars, galaxies) depend mainly on five of them: $m_e,$ $m_u,$ $m_d,$ α, and ${\alpha }_G$ (where $m_{\mathrm{proton}}$ and ${\alpha }_{\mathrm{QCD}}$ are taken as defined quantities). Three of these appear to be independent in the context of Grand Unified Theories (that is, not fixed by any known symmetry) and at the same time have values within a very narrow window which provides for stable nucleons and nuclei and abundant carbon. The conjecture is made that the two light quark masses and one coupling constant are ultimately determined even in the “final theory” by a choice from a large or continuous ensemble, and the prediction is offered that the correct unification scheme will not allow calculation of ${(m}_d-m_u{)/m}_{\mathrm{proton}}$ from first principles alone.

The top quark, discovered at the Fermilab Tevatron collider in 1995, is the heaviest known elementary particle. Its large mass suggests that it may play a special role in nature. It behaves differently from the other known quarks due to both its large mass and its short lifetime. Thus far we have only crude measurements of the properties of the top quark, such as its mass, weak interactions, strong interactions, and decay modes. These measurements will be made more precise when the Tevatron begins operation again in 2001. I review the present status of these measurements, and discuss their anticipated improvement.

This paper discusses speculative disaster scenarios inspired by hypothetical new fundamental processes that might occur in high-energy relativistic heavy-ion collisions. The authors estimate the parameters relevant to black-hole production and find that they are absurdly small. They show that other accelerator and (especially) cosmic-ray environments have already provided far more auspicious opportunities for transition to a new vacuum state, so that existing observations provide stringent bounds. The possibility of producing a dangerous strangelet is discussed in most detail. The authors argue that four separate requirements are necessary for this to occur: existence of large stable strangelets, metastability of intermediate size strangelets, negative charge for strangelets along the stability line, and production of intermediate size strangelets in the heavy ion environment. Both theoretical and experimental reasons why each of these appears unlikely are discussed. In particular, the authors know of no plausible suggestion for why the third or especially the fourth might be true. Given minimal physical assumptions, the continued existence of the Moon, in the form we know it, despite billions of years of cosmic-ray exposure, provides powerful empirical evidence against the possibility of dangerous strangelet production.

80 years ago, Joseph Larmor planted the seed that grew into today’s imposing body of knowledge about how the Earth’s magnetic field is created. His simple idea, that the geomagnetic field is the result of dynamo action in the Earth’s electrically conducting, fluid core, encountered many difficulties, but these have by now been largely overcome, while alternative proposals have been found to be untenable. The development of the theory and its current status are reviewed below. The basic electrodynamics are summarized, but the main focus is on dynamical questions. A special study is made of the energy and entropy requirements of the dynamo and in particular of how efficient it is, considered as a heat engine. Particular attention is paid to modeling core magnetohydrodynamics in a way that is tractable but nevertheless incorporates the dynamical effects of core turbulence in an approximate way. This theory has been tested by numerical integrations, some results from which are presented. The success of these simulations seems to be considerable, when measured against the known geomagnetic facts summarized here. Obstacles that still remain to be overcome are discussed, and some other future challenges are described.

This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling electrostatics and electronic structure methods is first discussed. Then the basic aspects of real-space representations are presented. Multigrid techniques for solving the discretized problems are covered; these numerical schemes allow for highly efficient solution of the grid-based equations. Applications to problems in electrostatics are discussed, in particular, numerical solutions of Poisson and Poisson-Boltzmann equations. Next, methods for solving self-consistent eigenvalue problems in real space are presented; these techniques have been extensively applied to solutions of the Hartree-Fock and Kohn-Sham equations of electronic structure, and to eigenvalue problems arising in semiconductor and polymer physics. Finally, real-space methods have found recent application in computations of optical response and excited states in time-dependent density-functional theory, and these computational developments are summarized. Multiscale solvers are competitive with the most efficient available plane-wave techniques in terms of the number of self-consistency steps required to reach the ground state, and they require less work in each self-consistency update on a uniform grid. Besides excellent efficiencies, the decided advantages of the real-space multiscale approach are (1) the near-locality of each function update, (2) the ability to handle global eigenfunction constraints and potential updates on coarse levels, and (3) the ability to incorporate adaptive local mesh refinements without loss of optimal multigrid efficiencies.

Radiative transfer has been studied for almost a century, but only recently have effects of broken symmetry in the diffusion of light been systematically studied. Familiar concepts such as the mean free path and the diffusion constant must be generalized. Nematic liquid crystals provide a realistic complex system in which the new concepts are relevant. Thermal fluctuations of the local optical axis generate a weak but very specific and anisotropic light scattering and can even be long range. In addition, two different modes of electromagnetic propagation exist, with different polarization, and with different speeds, that couple in multiple scattering. It becomes a challenge to describe optical phenomena such as birefringence, interference, polarization, and intensity fluctuations under such conditions. In this review, the authors first describe the interesting phenomena in radiative transfer in complex anisotropic media and nematic liquid crystals. They then develop the systematic theory of transport starting from the fundamental equations and going through a Green’s-function formulation.

The striking similarity of ac conduction in quite different disordered solids is discussed in terms of experimental results, modeling, and computer simulations. After giving an overview of experiment, a macroscopic and a microscopic model are reviewed. For both models the normalized ac conductivity as a function of a suitably scaled frequency becomes independent of details of the disorder in the extreme disorder limit, i.e., when the local randomly varying mobilities cover many orders of magnitude. The two universal ac conductivities are similar, but not identical; both are examples of unusual non-power-law universalities. It is argued that ac universality reflects an underlying percolation determining dc as well as ac conductivity in the extreme disorder limit. Three analytical approximations to the universal ac conductivities are presented and compared to computer simulations. Finally, model predictions are briefly compared to experiment.

The dramatic recent advances in molecular biology, which have opened a new era in medicine and biotechnology, rely on improved techniques to study large molecules. Electrophoresis is one of the most important of these. Separation of DNA by size, in particular, is at the heart of genome mapping and sequencing and is likely to play an increasing role in diagnosis. This article reviews, from the point of view of a physicist, the mechanisms responsible for electrophoretic separation of polyelectrolytes. This separation is mainly performed in gels, and a wide variety of migration mechanisms can come into play, depending on the polyelectrolyte’s architecture, on the electric fields applied, and on the properties of the gel. After a brief review of the thermodynamic and electrohydrodynamic principles relating to polyelectrolyte solutions, the author treats the phenomenology of electrophoresis and describes the conceptual and theoretical tools in the field. The reptation mechanisms, by which large flexible polyelectrolytes thread their way through the pores of the gel matrix, play a prominent role. Biased reptation, the extension of this model to electrophoresis, provides a very intuitive framework within which numerous physical ideas can be introduced and discussed. It has been the most popular theory in this domain, and it remains an inspiring concept for current development. There have also been important advances in experimental techniques such as single-molecule viodeomicroscopy and the development of nongel separation media and mechanisms. These, in turn, form the basis for fast-developing and innovative technologies like capillary electrophoresis, electrophoresis on microchips, and molecular ratchets.

The authors present a review of recent muon spin rotation (μSR) studies of the vortex state in type-II superconductors. There are significant gaps in our understanding of this unusual phase of matter, especially in unconventional superconductors, for which the description of the vortex structure is a subject of great controversy. The μSR technique provides a sensitive local probe of the spatially inhomogeneous magnetic field associated with the vortex state. For the case of a regular vortex lattice, the magnetic penetration depth λ and the coherence length ξ can be simultaneously extracted from the measured internal field distribution. The penetration depth is directly related to the density of superconducting carriers in the material, and measurements of its variation with temperature, magnetic field, and impurities can provide essential information on the symmetry of the order parameter. The coherence length measured with μSR is the length scale for spatial variations of the order parameter within a vortex core. A primary goal of this review article is to show that measurements of these fundamental length scales are fairly robust with respect to the details of how the field distribution is modeled. The reliability of the results is demonstrated by a comparison of the μSR experiments with relevant theories and with other experimental techniques. The authors also review μSR measurements that have focused on the study of pinning-induced spatial disorder and vortex fluctuation phenomena. The μSR technique has proven to be a powerful tool for investigating exotic vortex phases, where vortex transitions are directly observable from changes in the μSR line shape. Particular emphasis is given to μSR experiments performed on high-temperature superconductors since high-quality single crystals have become available.

The nuclear shell model predicts that the next doubly magic shell closure beyond ${}^{208}\mathrm{Pb}$ is at a proton number between $Z=114\mathrm{}$ and 126 and at a neutron number $N=184.\mathrm{}$ The outstanding aim of experimental investigations is the exploration of this region of spherical superheavy elements (SHE’s). This article describes the experimental methods that led to the identification of elements 107 to 112 at GSI, Darmstadt. Excitation functions were measured for the one-neutron evaporation channel of cold-fusion reactions using lead and bismuth targets. The maximum cross section was measured at beam energies well below a fusion barrier estimated in one dimension. These studies indicate that the transfer of nucleons is an important process for the initiation of fusion. The recent efforts at JINR, Dubna, to investigate the hot-fusion reaction for the production of SHE’s using actinide targets are also presented. First results were obtained on the synthesis of neutron-rich isotopes of elements 112 and 114. However, the most surprising result was achieved in 1999 at LBNL, Berkeley. In a study of the reaction ${}^{86}{\mathrm{K}\mathrm{r}+}^{208}{\mathrm{Pb}\to }^{294}{118}^{*},$ three decay chains were measured and assigned to the superheavy nucleus ${}^{293}118.$ The decay data reveal that, for the heaviest elements, the dominant decay mode is alpha emission, not fission. The results are discussed in the framework of theoretical models. This article also presents plans for the further development of the experimental setup and the application of new techniques. At a higher sensitivity, the exploration of the region of spherical SHE’s now seems to be feasible, more than 30 years after its prediction.

The authors define “ultrahigh-energy cosmic rays” (UHECRs) as those cosmic rays with energies above ${10}^{18}\mathrm{eV}.$ It had been anticipated that there would be a cutoff in the energy spectrum of primary cosmic rays around $6\times {10}^{19}\mathrm{eV}$ induced by the interaction of the particles with the 2.7-K primordial photons. However, recent experimental data have established that particles exist with energies greatly exceeding this. It follows that the sources of such particles are probably nearby, on a cosmological scale. However, although the trajectories of such energetic particles through the galactic and intergalactic magnetic fields may be nearly rectilinear, no astronomical sources have as yet been identified. This is the enigma of the highest-energy cosmic rays. The paper reviews the history of research in this energy regime and critically assesses the observational results on the energy spectrum, arrival directions, and composition of the primary cosmic rays based on observations made by six experiments. The detection methods currently available are described. Special techniques have been developed as particles of ${10}^{20}\mathrm{eV}$ or higher occur at a rate of only about 1 per ${\mathrm{km}}^2$ per century. Errors in measurement are given particular attention. The authors also review the theoretical predictions for a number of candidate sources of cosmic rays beyond the predicted cutoff. Finally, the four major projects planned to address the question of the origin of UHECRs are briefly described.