The time-dependent variational principle for many-body trial states is used to discuss the relation between the approaches of different molecular-dynamics models that describe indistinguishable fermions. Early attempts to include effects of the Pauli principle by means of nonlocal potentials, as well as more recent models that work with antisymmetrized many-body states, are reviewed under these premises.

Dramatic advances in the understanding of x-ray absorption fine structure (XAFS) have been made over the past few decades, which have led ultimately to a highly quantitative theory. This review covers these developments from a unified multiple-scattering viewpoint. The authors focus on extended x-ray absorption fine structure (EXAFS) well above an x-ray edge, and, to a lesser extent, on x-ray absorption near-edge structure (XANES) closer to an edge. The discussion includes both formal considerations, derived from a many-electron formulation, and practical computational methods based on independent-electron models, with many-body effects lumped into various inelastic losses and energy shifts. The main conceptual issues in XAFS theory are identified and their relative importance is assessed; these include the convergence of the multiple-scattering expansion, curved-wave effects, the scattering potential, inelastic losses, self-energy shifts, and vibrations and structural disorder. The advantages and limitations of current computational approaches are addressed, with particular regard to quantitative experimental comparisons.

Shear flow turbulence is a complex and interesting phenomenon which has been well known for a long time. The story of the physical understanding of its onset is a marvellous and recent tale of a unique nonlinearity. It is the convection term $\left(\mathbf{u}\cdot \mathbf{\nabla }\right)\mathbf{u}$ in the equation of motion which rules the transition to turbulence by introducing a subtle interplay between the nonnormal bunching of flow perturbations and their nonlinear interaction. By nonnormal coupling to the basic laminar flow, those disturbances which are misfit to the eigendirections can transiently draw energy from the laminar shear flow and grow before they ultimately fade away. If their intermediate growth is strong enough, they interact nonlinearly. This interaction recreates new misfit flow amplitudes, which again start drawing energy, grow transiently, interact, etc. This feedback loop is able to sustain a flow which, as a consequence of the nonlinearity, is spatiotemporally deterministic and irregular at the same time. We call this flow turbulent. The feedback mechanism has to be contrasted to that of a common instability. The laminar flow stays linearly stable, all eigenvalues have negative, damping real parts. That is, laminar shear flow passes to turbulence without (linear) instability. The onset of turbulence is the nonnormal-nonlinear performance of many degrees of freedom and not merely of a single, unstable one. Both features are mediated by the convective nonlinearity.

A classical thermodynamic description of a surface requires the introduction of a number of energetic parameters related to the surface steps. These parameters are the step free energy, the kink creation energy, and the energetic and entropic interactions between steps. This review will demonstrate how a statistical analysis of scanning tunneling microscopy images of stepped surfaces can provide appropriate values of these fundamental energetic parameters. The Si(001) surface is used as a model system. In order to illustrate the significance of these energetic parameters, two morphological surface phase transitions are discussed, namely, the thermal roughening transition and the orientational phase diagram.

The rise time of intense radiation determines the maximum field strength atoms can be exposed to before their polarizability dramatically drops due to the detachment of an outer electron. Recent progress in ultrafast optics has allowed the generation of ultraintense light pulses comprising merely a few field oscillation cycles. The arising intensity gradient allows electrons to survive in their bound atomic state up to external field strengths many times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency, resulting in a significant extension of the frontiers of nonlinear optics and (nonrelativistic) high-field physics. Implications include the generation of coherent harmonic radiation up to kiloelectronvolt photon energies and control of the atomic dipole moment on a subfemtosecond $\left(1\mathrm{}{\mathrm{f}\mathrm{s}=10\mathrm{}}^{\mathrm{-}15}\mathrm{}\mathrm{s}\right)$ time scale. This review presents the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discusses the impact of these pulses on high-field physics. Particular emphasis is placed on high-order harmonic emission and single subfemtosecond extreme ultraviolet/x-ray pulse generation. These as well as other strong-field processes are governed directly by the electric-field evolution, and hence their full control requires access to the (absolute) phase of the light carrier. We shall discuss routes to its determination and control, which will, for the first time, allow access to the electromagnetic fields in light waves and control of high-field interactions with never-before-achieved precision.

Since the first attempts to calculate the helium ground state in the early days of Bohr-Sommerfeld quantization, two-electron atoms have posed a series of unexpected challenges to theoretical physics. Despite the seemingly simple problem of three charged particles with known interactions, it took more than half a century after quantum mechanics was established to describe the spectra of two-electron atoms satisfactorily. The evolution of the understanding of correlated two-electron dynamics and its importance for doubly excited resonance states is presented here, with an emphasis on the concepts introduced. The authors begin by reviewing the historical development and summarizing the progress in measuring the spectra of two-electron atoms and in calculating them by solving the corresponding Schrödinger equation numerically. They devote the second part of the review to approximate quantum methods, in particular adiabatic and group-theoretical approaches. These methods explain and predict the striking regularities of two-electron resonance spectra, including propensity rules for decay and dipole transitions of resonant states. This progress was made possible through the identification of approximate dynamical symmetries leading to corresponding collective quantum numbers for correlated electron-pair dynamics. The quantum numbers are very different from the independent particle classification, suitable for low-lying states in atomic systems. The third section of the review describes modern semiclassical concepts and their application to two-electron atoms. Simple interpretations of the approximate quantum numbers and propensity rules can be given in terms of a few key periodic orbits of the classical three-body problem. This includes the puzzling existence of Rydberg series for electron-pair motion. Qualitative and quantitative semiclassical estimates for doubly excited states are obtained for both regular and chaotic classical two-electron dynamics using modern semiclassical techniques. These techniques set the stage for a theoretical investigation of the regime of extreme excitation towards the three-body breakup threshold. Together with periodic orbit spectroscopy, they supply new tools for the analysis of complex experimental spectra.

This paper gives the 1998 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the subset of constants on which the complete 1998 set of recommended values is based. The 1998 set replaces its immediate predecessor recommended by CODATA in 1986. The new adjustment, which takes into account all of the data available through 31 December 1998, is a significant advance over its 1986 counterpart. The standard uncertainties (i.e., estimated standard deviations) of the new recommended values are in most cases about 1/5 to 1/12 and in some cases 1/160 times the standard uncertainties of the corresponding 1986 values. Moreover, in almost all cases the absolute values of the differences between the 1998 values and the corresponding 1986 values are less than twice the standard uncertainties of the 1986 values. The new set of recommended values is available on the World Wide Web at physics.nist.gov/constants.

In colliding-beam facilities, the “final-focus system” must demagnify the beams to attain the very small spot sizes required at the interaction points. The first final-focus system with local chromatic correction was developed for the Stanford Linear Collider, where very large demagnifications were desired. This same conceptual design has been adopted by all of the future linear collider designs as well as the Superconducting Super Collider, the Stanford and KEK B Factories, and the proposed Muon Collider. In this paper, the overall layout, physics constraints, and optimization techniques relevant to the design of final-focus systems for high-energy electron-positron linear colliders are reviewed. Finally, advanced concepts to avoid some of the limitations of these systems are discussed.

The real part of ${\varepsilon }^{\prime }/\varepsilon$ measures direct $\mathrm{CP}$ violation in the decays of neutral kaons into two pions. This is a fundamental quantity that has justly attracted a great deal of theoretical as well as experimental work. Determination of its value may answer the question of whether $\mathrm{CP}$ violation is present only in the mass matrix of neutral kaons (the superweak scenario) or whether it is also at work directly in the decay amplitudes. After a brief historical summary, the present and expected experimental sensitivities are discussed. In light of these, the authors address the problem of estimating ${\varepsilon }^{\prime }/\varepsilon$ in the standard model and review the status of the theoretical predictions of ${\varepsilon }^{\prime }/\varepsilon$ as of the beginning of 1999. The short-distance part of the computation is now known to the next-to-leading order in QCD and QED and is therefore well under control. On the other hand, the evaluation of the hadronic matrix elements of the relevant operators is where most of the theoretical uncertainty still resides. The authors analyze the results of the most extensive calculations to date. The values of the matrix-element parameters in the various approaches are discussed, together with the allowed range of quark mixing angles in the Cabibbo-Kobayashi-Maskawa matrix. All recent predictions of ${\varepsilon }^{\prime }/\varepsilon$ are summarized and compared. Because of the intrinsic uncertainties of the long-distance computations, values ranging from ${10}^{-4}$ to a few times ${10}^{-3}$ can be accounted for in the standard model. Since this range covers most of the present experimental uncertainty, it is unlikely that new-physics effects can be disentangled from the standard-model prediction.

Photons have many advantages for vaporizing condensed systems, and laser vaporization sources have a flexibility not available with other methods. These sources are applied to making thin films in the well-known technique of pulsed laser deposition (PLD). The vaporized material may be further processed through a pulsed secondary gas, lending the source additional degrees of freedom. Such pulsed-gas sources have long been exploited for fundamental studies, and they are very promising for film deposition, as an alternative to chemical vapor deposition or molecular beam epitaxy. The authors outline the fundamental physics involved and go on to discuss recent experimental findings.

Protein folding has become one of the most actively studied problems in modern molecular biophysics. Approaches to the problem combine ideas from the physics of disordered systems, polymer physics, and molecular biology. Much can be learned from the statistical properties of model heteropolymers, the chain molecules having different monomers in irregular sequences. Even in highly evolved proteins, there is a strong random element in the sequences, which gives rise to a statistical ensemble of sequences for a given folded shape. Simple analytic models give rise to phase transitions between random, glassy, and folded states, depending on the temperature T and the design temperature $T^{\mathrm{des}}$ of the ensemble of sequences. Besides considering the analytic results obtainable in a random-energy model and in the Flory mean-field model of polymers, the article reports on confirming numerical simulations.

Supersymmetry is one of the most plausible and theoretically motivated frameworks for extending the standard model. However, any supersymmetry in Nature must be a broken symmetry. Dynamical supersymmetry breaking (DSB) is an attractive idea for incorporating supersymmetry into a successful description of Nature. The study of DSB has recently enjoyed dramatic progress, fueled by advances in our understanding of the dynamics of supersymmetric field theories. These advances have allowed for direct analysis of DSB in strongly coupled theories, and for the discovery of new DSB theories, some of which contradict early criteria for DSB. The authors review these criteria, emphasizing recently discovered exceptions. They also describe, through many examples, various techniques for directly establishing DSB by studying the infrared theory, including both older techniques in regions of weak coupling and new techniques in regions of strong coupling. Finally, they present a list of representative DSB models, their main properties, and the relations among them.

Thin films and quasi-two-dimensional systems show a wide range of ordering effects and related pattern-formation phenomena. The origins of these phenomena can often be traced to competition between the atomic (or molecular) interactions in the system and the resulting inherent frustration of the system. In magnetic thin films, a wide range of magnetic structures are possible as a result of the competition between the long-ranged dipolar interactions and localized interactions. This article reviews recent experimental and theoretical work which has developed our understanding of ordering and pattern formation in these films and in related structures.

The spectacular progress made during the last few years in reaching high energy densities in fast implosions of annular current sheaths (fast Z pinches) opens new possibilities for a broad spectrum of experiments, from x-ray generation to controlled thermonuclear fusion and astrophysics. At present Z pinches are the most intense laboratory x-ray sources (1.8 MJ in 5 ns from a volume 2 mm in diameter and 2 cm tall). Powers in excess of 200 TW have been obtained. This warrants summarizing the present knowledge of physics that governs the behavior of radiating, current-carrying plasma in fast Z pinches. This survey covers essentially all aspects of the physics of fast Z pinches: initiation, instabilities of the early stage, magnetic Rayleigh-Taylor instability in the implosion phase, formation of a transient quasiequilibrium near the stagnation point, and rebound. Considerable attention is paid to the analysis of hydrodynamic instabilities governing the implosion symmetry. Possible ways of mitigating these instabilities are discussed. Nonmagnetohydrodynamic effects (anomalous resistivity, generation of particle beams, etc.) are summarized. Various applications of fast Z pinches are briefly described. Scaling laws governing development of more powerful Z pinches are presented.

The role of stable shear flow in suppressing turbulence and turbulent transport in plasmas and neutral fluids is reviewed. Localized stable flow shear produces transport barriers whose extensive and highly successful utilization in fusion devices has made them the primary experimental technique for reducing and even eliminating the rapid turbulent losses of heat and particles that characterize fusion-grade plasmas. These transport barriers occur in different plasma regions with disparate physical properties and in a range of confining configurations, indicating a physical process of unusual universality. Flow shear suppresses turbulence by speeding up turbulent decorrelation. This is a robust feature of advection whenever the straining rate of stable mean flow shear exceeds the nonlinear decorrelation rate. Shear straining lowers correlation lengths in the direction of shear and reduces turbulent amplitudes. It also disrupts other processes that feed into or result from turbulence, including the linear instability of important collective modes, the transport-producing correlations between advecting fluid and advectants, and large-scale spatially connected avalanchelike transport events. In plasmas, regions of stable flow shear can be externally driven, but most frequently are created spontaneously in critical transitions between different plasma states. Shear suppression occurs in hydrodynamics and represents an extension of rapid-distortion theory to a long-time-scale nonlinear regime in two-dimensional stable shear flow. Examples from hydrodynamics include the emergence of coherent vortices in decaying two-dimensional Navier-Stokes turbulence and the reduction of turbulent transport in the stratosphere.

One of the major developments of twentieth-century physics has been the gradual recognition that a common feature of the known fundamental interactions is their gauge structure. In this article the authors review the early history of gauge theory, from Einstein’s theory of gravitation to the appearance of non-Abelian gauge theories in the fifties. The authors also review the early history of dimensional reduction, which played an important role in the development of gauge theory. A description is given of how, in recent times, the ideas of gauge theory and dimensional reduction have emerged naturally in the context of string theory and noncommutative geometry.

The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. The authors show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations but changing sign under improper rotations) and must involve three-point correlations that only come into play when the molecule has at least four atoms. In general, a molecule is characterized by an infinite set of chiral parameters. The authors illustrate the fact that these parameters can have differing signs and can vanish at different points as a molecule is continuously deformed into its mirror image. From this it is concluded that handedness is not an absolute concept but depends on the property being observed. Within a simplified model of classical interactions, the chiral parameter of the constituent molecules that determines the macroscopic pitch of cholesterics is identified.