The authors summarize existing experimental and theoretical knowledge of the structure function $F_2$ in the region of low $Q^2$ and low $x$. Constraints on the behavior of structure functions in the limit of $Q^2=0\mathrm{}$ are listed. Phenomenological low-$Q^2$ parametrizations of $F_2$ are collected, and their dynamical content is discussed. High-energy photoproduction and nuclear shadowing are described briefly. A recent update of the low-$Q^2$, low-$x$ experimental data and their implications is given.

The history of the proposal that solitons be used for optical fiber communications and of the technical developments toward making soliton transmission practical is reviewed. The causes of bit errors in long-distance soliton transmission are presented and the methods for reducing them are described. A perturbation theory suited for soliton analysis is developed. Current status and future prospects of long-distance repeaterless fiber communications are stated.

The experimental and theoretical evidence for intrinsic reflection-asymmetric shapes in nuclei is reviewed. The theoretical methods discussed cover a wide spectrum, from mean-field theory and its extensions to algebraic and cluster approaches. The experimental data for nuclear ground states and at low and high spin, cited as evidence for reflection asymmetry, are collected and categorized. The extensive data on electric dipole transition moments and their theoretical interpretation are surveyed, along with available data on electric octupole moments. The evidence for reflection-asymmetric molecular states in light nuclei is summarized. The application of reflection-asymmetric theories to descriptions of the fission barrier, bimodal fission, superdeformation, and hyperdeformations is reviewed, and some other perspectives in the wider context of nuclear physics are also given. [S0034-6861(96)00102-X]

Ultracold neutrons, that is, neutrons whose energy is so low that they can be contained for long periods of time in material and magnetic bottles, provide the basis for the currently most sensitive experiments seeking to detect the neutron electric dipole moment and to measure the neutron lifetime. The goal of this article is to review the work that has been done to date in applying ultracold neutrons to the study of condensed matter and to discuss the future prospects for this type of research. [S0034-6861(96)00202-4]

Exploration of the outer solar system has led to studies in a new area of physics: electronically induced sputtering of low-temperature, condensed-gas solids (ices). Many of the icy bodies in the outer solar system were found to be bombarded by relatively intense fluxes of ions and electrons, causing both changes in their optical reflectance and ejection (sputtering) of molecules from their surfaces. The small cohesive energies of the condensed-gas solids afford relatively large sputtering rates from the electronic excitations produced in the solid by fast ions and electrons. Such sputtering produces an ambient gas about an icy body, often the source of the local plasma. This colloquium outlines the physics of the sputtering of ices and its relevance to several outer-solar-system phenomena: the sputter-produced plasma trapped in Saturn's magnetosphere; the ${\mathrm{O}}_2$ atmosphere on Europa; and optical absorption features such as S${\mathrm{O}}_2$ in the surface of Europa and ${\mathrm{O}}_2$ and, possibly, ${\mathrm{O}}_3$ in the surface of Ganymede.

The current status of analytic higher-order perturbative computations of total cross sections and decay widths in Quantum Chromodynamics is reviewed. Important issues are the methodology of renormalization-group evaluations, the ambiguities of the renormalization scheme and its scale, and the technical challenge of calculating many-loop diagrams. As examples, the authors consider the quantities ${\sigma }_{\mathrm{tot}}(e^{+}{e}^{-}\to \mathrm{hadrons})$ and $\Gamma ({\tau }^{-}\to {\nu }_{\tau }+\mathrm{hadrons})$ up to $O\left({\alpha }_s^3\right)$ as well as $\Gamma (H\to \mathrm{hadrons})$ up to $O\left({\alpha }_s^2\right)$. The evaluation of the four-loop QED beta function is also described. The problem of theoretical uncertainty estimates in perturbative calculations is briefly discussed.

Plasmas that cool by radiation may become unstable to the formation of localized regions of lower temperature and increased density. Such radiative condensations are common in astrophysical and laboratory plasmas that are optically thin. Some perspective of the rapidly developing theoretical understanding of the dynamics of radiative condensations can be given in the framework of simple models. Radiative condensations are closely related to the condensation mode of the thermal instability, first studied by G. B. Field. Progress in the analysis of the nonlinear stage of this instability, achieved recently, employs the hierarchy of time and length scales of the problem. Sets of reduced equations, which describe the nonlinear dynamics of the radiative condensation, have been developed separately in the long-, intermediate-, and short-wavelength limits. Being quite different, all these reduced models predict radiation-driven segregation of the unstable plasma into two different states ("phases") on an intermediate time scale. Subsequent long-time evolution of radiative condensation may strongly depend on the type of boundary condition for the plasma. Radiative condensations usually disappear on a longer (thermal conduction related) time scale, if an inflow/outflow of the plasma is allowed. In this case, regions occupied by one of the "phases" expand until they occupy the whole plasma. On the contrary, in confined plasmas (no inflow/outflow of the plasma is allowed), radiative condensations can persist "forever." Similarities have been explored between radiative condensations and a number of instabilities of growth, such as the Darrieus-Landau instability and Ostwald ripening. A new type of shock wave with a nonmonotonic pressure profile, resulting from radiative condensation dynamics, is described. The role of magnetic fields in radiative condensations is briefly discussed.

A theory is given for the ground-state properties of short-ranged interacting spin-½ fermions moving in a periodic potential, based on a combination of renormalization-group ideas, the harmonic (Luttinger) liquid approach, and the symmetry properties of the Hubbard model, for a wide range of interactions and arbitrary fillings. For rational filling factors the outcome depends nontrivially on the parity of the order of the $2k_F$ umklapp scattering: even values fall into a universality class characterized by a separation of charge and spin degrees of freedom in the long-wavelength limit, while the action for the case of odd orders does not have this property, thus leading to distinct phase diagrams. It is argued that even when the long-wavelength action does exhibit a spin-charge separation it is not always an accurate approximation, particularly for the case of strong repulsion between electrons of the same spin. This leads to a classification of the possible ground states, associated correlation exponents, and phase transitions. The translational correlation exponents upon approaching insulator phases (existing at exact commensuration) by changing electron density can be related to the fractional charge of the solitons, using the Landauer rule.

We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

The author reviews methods for generating sub-Poissonian light and related concepts. This light has energy fluctuations reduced below the level which corresponds to a classical Poissonian process (shot-noise level). After an introduction to the concept of nonclassical light, an overview is given of the main methods of quantum-noise reduction. Sub-Poissonian processes are exemplified in different areas of optics, ranging from single-atom resonance fluorescence to nonlinear optics, laser physics, and cavity quantum electrodynamics. Emphasis is placed on the conceptual foundations, and on developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-Poissonian light generation in lasers and masers. The sources of quantum noise in these devices are analyzed, and four noise-suppression methods are discussed in detail: regularization of the pumping, suppression of spontaneous-emission noise, nonadiabatic evolution of the atomic variables, and twin-beam generation.

The history of the theory of quantum nondemolition (QND) measurements from the 1920s until today is reviewed. The definition and main principles of QND measurements are outlined. Achievements in the experimental realization of QND measurements and several new promising schemes of QND measurements are described. A list of the most important problems (from the authors' point of view) in the area of QND measurements is presented. The problem of measurement of a quantum oscillator phase is considered. A new method of phase measurement is proposed. Examples of possible solutions of fundamental physical problems using QND methods are given.

The authors review the experimental measurements and theoretical descriptions of leptonic and semileptonic decays of particles containing a single heavy quark, either charm or bottom. Measurements of bottom semileptonic decays are used to determine the magnitudes of two fundamental parameters of the standard model, the Cabibbo-Kobayashi-Maskawa matrix elements $V_{\mathrm{cb}}$ and $V_{\mathrm{ub}}$. These parameters are connected with the physics of quark flavor and mass, and they have important implications for the breakdown of $\mathrm{CP}$ symmetry. To extract precise values of $\left|V_{\mathrm{cb}}\right|$ and $\left|V_{\mathrm{ub}}\right|$ from measurements, however, requires a good understanding of the decay dynamics. Measurements of both charm and bottom decay distributions provide information on the interactions governing these processes. The underlying weak transition in each case is relatively simple, but the strong interactions that bind the quarks into hadrons introduce complications. The authors also discuss new theoretical approaches, especially heavy-quark effective theory and lattice QCD, which are providing insights and predictions now being tested by experiment. An international effort at many laboratories will rapidly advance knowledge of this area of physics during the next decade.

The scanning acoustic microscope is a powerful new tool for the study of the physical properties of materials and has been successfully used for imaging interior structures and for nondestructive evaluation in materials science and biology. Its principles of operation, resolution, penetration ability, and contrast mechanisms are simply described in this paper. Recent progress in the application of acoustic microscopy to material characterization in solid materials is summarized. The experimental elastic microanalysis of bulk materials is carried out by measuring $V\left(z\right)\mathrm{}$, which includes examining the reflectance function of solid material, measuring the phase velocity and attenuation of leaky surface acoustic waves at the liquid-specimen boundary, and determining the elastic constants of the material. The layer thickness and mechanical properties of layered solids are studied by examining the dispersion properties of surface acoustic waves. A knowledge of the propagation properties of acoustic waves on the surface of materials is essential for understanding the contrast mechanisms and quantitative measurements in acoustic microscopy; these propagation properties are thus also briefly described in this paper. Finally, further developments of the scanning acoustic microscope aimed at improving its performance for quantitative evaluation are presented. These could expand the scope of the acoustic microscope as a diagnostic tool in many areas of science and technology.

When the analysis of absorption with mode conversion effects included began to mature in recent years, the study of the corresponding effects on emission began and has led to some surprising results. The classical expressions for cyclotron or synchrotron emission from a harmonic resonance were originally derived from models that did not include mode conversion or its attendant reflection, and classical expressions for the optical depth and opacity were obtained. When mode conversion was included, the principal surprise was that the transmission coefficient, which was understood as being due to absorption, is totally independent of absorption and due exclusively to tunneling. The other surprise from the mode conversion analysis is that the observed emission arises from two distinct sources, one direct and one from an indirect Bernstein wave source which is partially converted in the cyclotron layer to outgoing electromagnetic waves, with the net result that mode conversion cancels out for the electron case, but not for ions. The only corrections to electron cyclotron emission are then due to reflection effects, and these have been shown to be small for many laboratory plasmas, leading to the validation of the classical formula for these cases, but via an entirely new paradigm in its interpretation. This review includes a summary of the absorption process for both electron and ion cyclotron harmonics, and reviews carefully the emission physics, including both potential error estimates and a discussion of the emission source distribution in space.

During the last 20 years, magnetically confined laboratory plasmas of steadily increasing temperatures and densities have been obtained, most notably in tokamak configurations, and now approach the conditions necessary to sustain a fusion reaction. Even more important to the goal of understanding the physics of such systems, remarkable advances in plasma diagnostics, the techniques for determining the properties of such plasmas, have accompanied these developments. More parameters can be determined with greater accuracy and finer spatial and temporal resolution. The magnetic configuration, the primary local thermodynamic quantities (density, temperature, and drift velocity), and other necessary quantities can now be measured with sufficient accuracy to determine particle and energy fluxes within the plasma and to characterize the basic transport processes. These plasmas are far from thermodynamic equilibrium. This deviation manifests itself in a variety of instabilities on several spatial and temporal scales, many of which are aptly described as turbulence. Many aspects of the turbulence can also be characterized. This article reviews the current state of diagnostics from an epistemological perspective: the capabilities and limitations for measuring each important physical quantity are presented.

Helium and heavy-element diffusion are both included in precise calculations of solar models. In addition, improvements in the input data for solar interior models are described for nuclear reaction rates, the solar luminosity, the solar age, heavy-element abundances, radiative opacities, helium and metal diffusion rates, and neutrino interaction cross sections. The effects on the neutrino fluxes of each change in the input physics are evaluated separately by constructing a series of solar models with one additional improvement added at each stage. The effective $1\sigma$ uncertainties in the individual input quantities are estimated and used to evaluate the uncertainties in the calculated neutrino fluxes and the calculated event rates for solar neutrino experiments. The calculated neutrino event rates, including all of the improvements, are ${9.3}_{-1.4\mathrm{}}^{+1.2\mathrm{}}$ SNU for the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ experiment and ${137}_{-7\mathrm{}}^{+8\mathrm{}}$ SNU for the ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ experiments. The calculated flux of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ neutrinos is 5.1 (${1.00}_{-0.07\mathrm{}}^{+0.06\mathrm{}}$)×${10}^9$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\mathrm{s}}^{-1\mathrm{}}$ and the flux of ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ neutrinos is 6.6(${1.00}_{-0.17\mathrm{}}^{+0.14\mathrm{}}$)×${10}^6$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\mathrm{s}}^{-1\mathrm{}}$. The primordial helium abundance found for this model is $Y=0.278\mathrm{}$. The present-day surface abundance of the model is $Y_s=0.247\mathrm{}$, in agreement with the helioseismological measurement of $Y_s=0.242\mathrm{}\pm 0.003$ determined by Hernandez and Christensen-Dalsgaard (1994). The computed depth of the convective zone is $R=0.712\mathrm{}{R}_{\odot }$, in agreement with the observed value determined from $p$-mode oscillation data of $R=0.713\mathrm{}\pm 0.003R_{\odot }$ found by Christensen-Dalsgaard et al. (1991). Although the present results increase the predicted event rate in the four operating solar neutrino experiments by almost $1\sigma$ (theoretical uncertainty), they only slightly increase the difficulty of explaining the existing experiments with standard physics (i.e., by assuming that nothing happens to the neutrinos after they are created in the center of the sun). For an extreme model in which all diffusion (helium and heavy-element diffusion) is neglected, the event rates are ${7.0}_{-1.0\mathrm{}}^{+0.9\mathrm{}}$ SNU for the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ experiment and ${126}_{-6\mathrm{}}^{+6\mathrm{}}$ SNU for the ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ experiments, while the ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ neutrino fluxes are, respectively, 4.5(${1.00}_{-0.07\mathrm{}}^{+0.06\mathrm{}}$)×${10}^9$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\mathrm{s}}^{-1\mathrm{}}$ and 4.9(${1.00}_{-0.17\mathrm{}}^{+0.14\mathrm{}}$)×${10}^6$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\mathrm{s}}^{-1\mathrm{}}$. For the no-diffusion model, the computed value of the depth of the convective zone is $R=0.726\mathrm{}{R}_{\odot }$, which disagrees with the observed helioseismological value. The calculated surface abundance of helium, $Y_s=0.268\mathrm{}$, is also in disagreement with the $p$-mode measurement. The authors conclude that helioseismology provides strong evidence for element diffusion and therefore for the somewhat larger solar neutrino event rates calculated in this paper.

A precise form of the quantum-mechanical time-energy uncertainty relation is derived. For any given initial state (density operator), time-dependent Hamiltonian, and subspace of reference states, it gives upper and lower bounds for the probability of finding the system in a state in that subspace at a later or earlier time. The bounds involve only the initial data, the energy uncertainty in the initial state, and the energy uncertainty in the reference subspace. They describe how fast the state enters or leaves the reference subspace. They are exact if, but not only if, the initial state or the projection onto the reference subspace commutes with the Hamiltonian. The basic tool used in the proof is a simple inequality for expectation values of commutators, which generalizes the usual uncertainty relation. By introducing suitable comparison dynamics (trial propagators), the bounds can be made arbitrarily tight. They represent a time-dependent variational principle, in terms of trial propagators, which provides explicit error estimates and reproduces the exact time evolution when one varies over all trial propagators. As illustrations, we derive accurate lower bounds on the escape time of a particle out of a potential well modeling a quantum dot, and the total time before which a ${\mathrm{He}}^{+}$ ion moving in a uniform magnetic field loses its electron.