The neutrinos that are produced in the solar fusion reaction chains reflect the conditions in the stellar interior. If the model predictions for the expected neutrino fluxes are firm, then the solar neutrino experiments can also test neutrino properties during propagation along the $1.5\times {10}^8\mathrm{kilometer}$ “baseline” between “source” and detector. So far, results have been acquired with five solar neutrino detectors: Homestake, Kamiokande, Superkamiokande, Gallex, and Sage. Taking all of the experimental data together, it appears that the abundant pp neutrinos are present, the moderately abundant ${}^7\mathrm{Be}$ neutrinos are strongly or totally suppressed, and the rare ${}^8\mathrm{B}$ neutrinos are partially reduced, by a factor of about three. This outcome cannot be explained by modifications of the stellar model but it is consistent with the hypothesis of neutrino flavor oscillations. Such oscillations could occur on the way between the solar core and the detector. In such a scenario, a nonvanishing neutrino rest mass would follow. The evidence is summarized here, and the outlook as regards anticipated future experiments is briefly discussed.

Reaction waves, in which an energy source sustains a wave front, occur in many areas of physics. The most important of them is a solitary wave or autowave, which is described on a coarse scale as a flamon, a surface separating zones. Mathematically, the waves are described by nonlinear transport equations, whose approximate solution gives propagation velocities of interfaces and stability criteria for the wave fronts. The instabilities of the autowave can produce complicated behavior such as periodic waves or spirals in two dimensions. Manifestations of the complex behavior include Gunn domains and cellular front structures. Important parameters that permit one to classify the wave and its stability are the Lewis number and the Zel’dovich number. A reaction wave can also have a more complicated inner structure, with several zones responsible for different physical properties.

A review is given of theoretical concepts and experimental results on spontaneous formation of periodically ordered nanometer-scale structures on crystal surfaces. Thermodynamic theory is reviewed for various classes of spontaneously ordered nanostructures, namely, for periodically faceted surfaces, for periodic surface structures of planar domains, and for ordered arrays of three-dimensional coherently strained islands. All these structures are described as equilibrium structures of elastic domains. Despite the fact that driving forces of the instability of a homogeneous phase are different in each case, the common driving force for the long-range ordering of the inhomogeneous phase is the elastic interaction. The theory of the formation of multisheet structures of islands is reviewed, which is governed by both equilibrium ordering and kinetic-controlled ordering. For the islands of the first sheet, an equilibrium structure is formed, and for the next sheets, the structure of the surface islands meets the equilibrium under the constraint of the fixed structures of the buried islands. The experimental situation for the fabrication technology of ordered arrays of semiconductor quantum dots is analyzed, including a discussion of both single-sheet and multiple-sheet ordered arrays.

Methods exhibiting linear scaling with respect to the size of the system, the so-called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms that take advantage of the decay properties of the density matrix. In this article the physical decay properties of the density matrix will first be studied for both metals and insulators. Several strategies for constructing O(N) algorithms will then be presented and critically examined. Some issues that are relevant only for self-consistent O(N) methods, such as the calculation of the Hartree potential and mixing issues, will also be discussed. Finally some typical applications of O(N) methods are briefly described.

When an interacting many-body system, such as a magnet, is driven in time by an external perturbation, such as a magnetic field, the system cannot respond instantaneously due to relaxational delay. The response of such a system under a time-dependent field leads to many novel physical phenomena with intriguing physics and important technological applications. For oscillating fields, one obtains hysteresis that would not occur under quasistatic conditions in the presence of thermal fluctuations. Under some extreme conditions of the driving field, one can also obtain a nonzero average value of the variable undergoing such “dynamic hysteresis.” This nonzero value indicates a breaking of the symmetry of the hysteresis loop about the origin. Such a transition to the “spontaneously broken symmetric phase” occurs dynamically when the driving frequency of the field increases beyond its threshold value, which depends on the field amplitude and the temperature. Similar dynamic transitions also occur for pulsed and stochastically varying fields. We present an overview of the ongoing research in this not-so-old field of dynamic hysteresis and transitions.

The motion of planetary bodies is the archetypal clockwork system. Indeed, clocks and calendars were developed to keep track of the relative motions of the Earth, the Sun, and the Moon. However, studies over the past few decades imply that this predictable regularity does not extend to small bodies, nor does it apply to the precise trajectories of the planets themselves over long timescales.

The study of subtle interactions in atomic and molecular systems has stirred scientific curiosity since the dawn of quantum mechanics. Even today, research into perturbative long-range interactions continues to push into new territory, driven largely by the experimental capabilities of Rydberg state spectroscopy to detect effects of extremely weak interactions. While static long-range multipole interactions have been studied for years, the presence of dynamic terms that involve both position and momentum operators has been demonstrated only surprisingly recently. In this paper we document the existence of an effective vector interaction term in the long-range potential experienced by a moving charged particle in the presence of an anisotropic ionic core. In contrast to ordinary static quadrupole or dipole interaction terms, the existence of this vector interaction hinges on the motion of the distant charge as it roams beyond the confines of the core.

Lipid monolayers on the surface of water have been studied for over a hundred years, but in the last decade there has been a dramatic evolution in our understanding of the structures and phase transitions of these systems, driven by new experimental techniques and theoretical advances. In this review, dense monolayers of simple lipids are described in detail, including structures revealed by x-ray-diffraction experiments, computer simulations, molecular models, and a phenomenological theory of phase transitions. The effects of chirality and the structures of phospholipid monolayers are considered. Open questions and possible approaches to finding answers are discussed.

Drift waves occur universally in magnetized plasmas producing the dominant mechanism for the transport of particles, energy and momentum across magnetic field lines. A wealth of information obtained from quasistationary laboratory experiments for plasma confinement is reviewed for drift waves driven unstable by density gradients, temperature gradients and trapped particle effects. The modern understanding of Bohm transport and the role of sheared flows and magnetic shear in reducing the transport to the gyro-Bohm rate are explained and illustrated with large scale computer simulations. The types of mixed wave and vortex turbulence spontaneously generated in nonuniform plasmas are derived with reduced magnetized fluid descriptions. The types of theoretical descriptions reviewed include weak turbulence theory, Kolmogorov anisotropic spectral indices, and the mixing length. A number of standard turbulent diffusivity formulas are given for the various space-time scales of the drift-wave turbulent mixing.

This review discusses the heavy-electron compounds and related materials from the perspective of their electrodynamic response. The investigation of the electrodynamic response by means of optical methods, extending over a very broad spectral range, should reveal, in principle, the complete excitation spectrum. This study incorporates several important sources of information on the intrinsic properties of the investigated materials. In particular, attention will be focused on the optical properties of prototype heavy-electron systems and on Kondo systems with low-temperature non-Fermi-liquid behavior or insulating characteristics. In the discussion, the electrodynamic response will be related to other relevant results arrived at by various experimental methods and to the theoretical state of the art.

The advent of high-$T_c$ superconductors gave great impetus to the development of thin-film superconducting quantum interference devices (SQUIDs) for operation at temperatures up to the boiling point of liquid nitrogen, 77 K. The spectral density of the white flux noise can be calculated analytically for rf SQUIDs and by computer simulation for dc SQUIDs; however, observed noise spectral densities are typically an order of magnitude higher. Low-frequency $1/f$ noise from thermally activated vortex motion is a much bigger issue in high-$T_c$ SQUIDs at 77 K than in low-$T_c$ SQUIDs because of the low flux-pinning energies in high-$T_c$ superconductors. The magnitude of the noise depends strongly on the quality of the thin films, and much effort has been expended to improve techniques for depositing ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ (YBCO) on lattice-matched single-crystal substrates. Substantial effort has also been invested in the development of new types of Josephson junctions, of which grain-boundary junctions are the most widely used in SQUIDs. Appropriate electronic read-out schemes largely eliminate $1/f$ noise from fluctuations in the junction critical current in both rf and dc SQUIDs. Typical levels of white flux noise are a few $\mu {\Phi }_0{\mathrm{Hz}}^{\mathrm{-}1/2}$ (${\Phi }_0$ is the flux quantum). Magnetometers—consisting of a superconducting flux transformer coupled to a SQUID—achieve a white magnetic-field noise as low as 10 fT ${\mathrm{Hz}}^{\mathrm{-}1/2}$, increasing to typically 30 fT ${\mathrm{Hz}}^{\mathrm{-}1/2}$ at 1 Hz. When these devices are operated in an unshielded environment, it is important to minimize the motion of trapped vortices and induced supercurrents, which can greatly increase the $1/f$ noise. The ambient noise is far greater than the intrinsic noise of the devices, but can be substantially reduced by various gradiometer configurations. There is now considerable effort to apply high-$T_c$ SQUIDs in magnetocardiology, nondestructive evaluation, microscopy, and geophysics.

The measurements of the properties of the $Z$ boson performed with the large data samples collected at LEP and SLC challenge the standard model of the electroweak interaction with unprecedented precision. The $Z$ mass is measured to 2 parts in ${10}^5,$ while other relevant electroweak observables such as the electroweak mixing angle, which is related to the strength of the neutral current, are measured with an accuracy of 1 part in ${10}^3.$ At this level of precision the effects of electroweak radiative corrections and in particular of the nontrivial loop contributions are visible. Assuming the validity of the standard model, the top mass can be predicted with a precision of about 10% and with a value in good agreement with the direct measurements. The global fit of electroweak data constrains the mass of the Higgs boson, giving an indirect indication of a relatively light Higgs. The overall agreement of the data with the predictions of the standard model is good, considerably limiting the room available for new physics. This paper describes the experimental techniques that led to such a thorough test of the electroweak theory. The basic theoretical concepts are reviewed and the measurements compared with theoretical predictions.

Top-quark condensation, in particular the minimal framework in which the neutral Higgs scalar is (predominantly) an effective $\overline{t}t$ condensate of the standard model, is reviewed. Computational approaches are compared and similarities, differences, and deficiencies pointed out. Extensions of the minimal framework, including scenarios with two composite Higgs doublets, additional neutrino condensates, and $\overline{t}t$ condensation arising from four-fermion interactions with enlarged symmetries, are described. Possible renormalizable models of underlying physics potentially responsible for the condensation, including topcolor-assisted technicolor frameworks, are discussed. Phenomenological implications of top condensate models are outlined. Outstanding theoretical issues and problems for future investigation are pointed out. Progress in the field after this article was accepted has been briefly covered in a Note added at the end.

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

Particle physics has evolved a coherent model that characterizes forces and particles at the most elementary level. This standard model, built from many theoretical and experimental studies, is in excellent accord with almost all current data. However, there are many hints that it is but an approximation to a yet more fundamental theory. The authors trace the development of the standard model and indicate the reasons for believing that it is incomplete.

The author discusses the general principles underlying quantum field theory and attempts to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality. A few of quantum field theory’s most striking successes, both achieved and prospective are mentioned, and possible limitations of the theory are viewed in the light of its history.