This review is addressed to the development of lasers that might generate coherent radiation at ultrashort wavelengths by stimulating recoilless nuclear transitions in solids. First, the authors review the basic physics of stimulated emission, superradiance and the kinetics of lasing, with particular attention to those aspects that characterize recoilless nuclear transitions in solid hosts. Then they classify the various approaches to pumping that have been proposed for resolving the “graser dilemma”—that the pump can destroy the conditions essential to gain—and discuss the general requirements for specification of an active nuclide and its solid host. The authors then classify and review those graser systems proposed since 1980 and prior to July 1996 in the published literature of the field, namely, (1) those that would pump directly, either with radiation or with intense bursts of neutrons; (2) those that would pump indirectly by first generating a nuclear isomer; (3) those that would eliminate the need for population inversion; and (4) several miscellaneous concepts. The significance of recent relevant experiments is described and discussed, and, finally, recommendations for future research are made.

The independent-particle model explains many features of atomic nuclei and other fermion systems. The low-energy states of nearly closed-shell systems can be interpreted as having quasiparticles in single-particle orbitals. The difference between physical particles and quasiparticles results from the effects of correlations in the system. In this Colloquium the authors consider the consequences of these correlations. They discuss in particular, mainly for the case of nuclei, the quasihole strength $z$ (spectroscopic factor) that gives the probability of the quasiparticle’s being a physical particle. Results from both theory and experiment indicate that $z\sim 0.65$ and imply that only $\sim 2/3$ of the time a nucleon acts as an independent particle bound in an average potential. The fraction of $\sim 1/3$ of correlated nucleons is larger than believed in the past.

Macroscopic thin liquid films are entities that are important in biophysics, physics, and engineering, as well as in natural settings. They can be composed of common liquids such as water or oil, rheologically complex materials such as polymers solutions or melts, or complex mixtures of phases or components. When the films are subjected to the action of various mechanical, thermal, or structural factors, they display interesting dynamic phenomena such as wave propagation, wave steepening, and development of chaotic responses. Such films can display rupture phenomena creating holes, spreading of fronts, and the development of fingers. In this review a unified mathematical theory is presented that takes advantage of the disparity of the length scales and is based on the asymptotic procedure of reduction of the full set of governing equations and boundary conditions to a simplified, highly nonlinear, evolution equation or to a set of equations. As a result of this long-wave theory, a mathematical system is obtained that does not have the mathematical complexity of the original free-boundary problem but does preserve many of the important features of its physics. The basics of the long-wave theory are explained. If, in addition, the Reynolds number of the flow is not too large, the analogy with Reynolds’s theory of lubrication can be drawn. A general nonlinear evolution equation or equations are then derived and various particular cases are considered. Each case contains a discussion of the linear stability properties of the base-state solutions and of the nonlinear spatiotemporal evolution of the interface (and other scalar variables, such as temperature or solute concentration). The cases reducing to a single highly nonlinear evolution equation are first examined. These include: (a) films with constant interfacial shear stress and constant surface tension, (b) films with constant surface tension and gravity only, (c) films with van der Waals (long-range molecular) forces and constant surface tension only, (d) films with thermocapillarity, surface tension, and body force only, (e) films with temperature-dependent physical properties, (f) evaporating/condensing films, (g) films on a thick substrate, (h) films on a horizontal cylinder, and (i) films on a rotating disc. The dynamics of the films with a spatial dependence of the base-state solution are then studied. These include the examples of nonuniform temperature or heat flux at liquid-solid boundaries. Problems which reduce to a set of nonlinear evolution equations are considered next. Those include (a) the dynamics of free liquid films, (b) bounded films with interfacial viscosity, and (c) dynamics of soluble and insoluble surfactants in bounded and free films. The spreading of drops on a solid surface and moving contact lines, including effects of heat and mass transport and van der Waals attractions, are then addressed. Several related topics such as falling films and sheets and Hele-Shaw flows are also briefly discussed. The results discussed give motivation for the development of careful experiments which can be used to test the theories and exhibit new phenomena.

Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of the 19th century. Linear stability theory governs the onset of breakup and was developed by Rayleigh, Plateau, and Maxwell. However, only recently has attention turned to the nonlinear behavior in the vicinity of the singular point where a drop separates. The increased attention is due to a number of recent and increasingly refined experiments, as well as to a host of technological applications, ranging from printing to mixing and fiber spinning. The description of drop separation becomes possible because jet motion turns out to be effectively governed by one-dimensional equations, which still contain most of the richness of the original dynamics. In addition, an attraction for physicists lies in the fact that the separation singularity is governed by universal scaling laws, which constitute an asymptotic solution of the Navier-Stokes equation before and after breakup. The Navier-Stokes equation is thus continued uniquely through the singularity. At high viscosities, a series of noise-driven instabilities has been observed, which are a nested superposition of singularities of the same universal form. At low viscosities, there is rich scaling behavior in addition to aesthetically pleasing breakup patterns driven by capillary waves. The author reviews the theoretical development of this field alongside recent experimental work, and outlines unsolved problems.

The periodic Anderson and Kondo lattice model describe the physics of conduction electrons in extended orbitals interacting with strongly correlated electrons in localized orbitals. These models are relevant for the so-called heavy-fermion and related systems such as the Kondo insulators. In this review we summarize recent progress in the understanding of these models, in particular, the one-dimensional Kondo lattice model. The ground-state phase diagram for the one-dimensional Kondo lattice model is determined and shows three distinct phases: a ferromagnetic metallic, an insulating spin liquid, and a paramagnetic metallic state. We present results on these phases obtained from rigorous and approximate analytical calculations supported by various extensive numerical studies on finite-size systems. The ferromagnetic phase appears in the limit of low density of conduction electrons and for strong Kondo coupling away from half filling. On the other hand, the half-filled Kondo lattice has a gap in both spin and charge excitations, i.e., it has a spin-liquid ground state. The paramagnetic phase may be considered as the generic heavy-fermion state and appears in the weak-coupling limit away from half filling. While the former two phases are well understood, the physics of the paramagnetic phase is not worked out in detail yet. In this context various questions will be considered here: Does the Fermi surface include conduction electrons only or also the localized electrons? Does the concept of Luttinger liquid apply in this case? The extension of these results to higher dimensions is also discussed. It is important to notice that the ground states of the Kondo lattice and the periodic Anderson model involve complicated effects, which cannot be understood by simple extension of the single- or two-impurity problem.

This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined region with a chaotic classical dynamics, which is coupled to two electron reservoirs via point contacts. The disordered wire also connects two reservoirs, either directly or via a point contact or tunnel barrier. One of the two reservoirs may be in the superconducting state, in which case conduction involves Andreev reflection at the interface with the superconductor. In the case of the quantum dot, the distribution of the scattering matrix is given by either Dyson’s circular ensemble for ballistic point contacts or the Poisson kernel for point contacts containing a tunnel barrier. In the case of the disordered wire, the distribution of the scattering matrix is obtained from the Dorokhov-Mello-Pereyra-Kumar equation, which is a one-dimensional scaling equation. The equivalence is discussed with the nonlinear $\sigma$ model, which is a supersymmetric field theory of localization. The distribution of scattering matrices is applied to a variety of physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction.

Spin-exchange optical pumping of mixtures of alkali-metal vapors and noble gases can be used to efficiently polarize the nuclei of the noble-gas atoms. Liters of noble gases at standard temperature and pressure and with nuclear spin polarizations of several tens of percent are now used in many applications. The authors describe the basic phenomena that govern the spin-exchange process and review the physics of angular momentum transfer and loss in optical pumping and spin-exchange collisions.

In this tutorial review a definition of the magnetization which can be used at the microscopic and quantum-mechanical level is motivated and developed. Its implications for the problem of reconstructing the magnetization in a crystal from magnetic neutron-diffraction data or from band-theoretical calculations are discussed, paying special attention to the relation between spin and orbital contributions.

Experimental studies of the superconductive properties of fullerides are briefly reviewed. Theoretical calculations of the electron-phonon coupling, in particular for the intramolecular phonons, are discussed extensively. The calculations are compared with coupling constants deduced from a number of different experimental techniques. It is discussed why ${\mathrm{A}}_3$${\mathrm{C}}_{60}$ are not Mott-Hubbard insulators, in spite of the large Coulomb interaction. Estimates of the Coulomb pseudopotential ${\mathrm{\mu }}^{\mathrm{*}}$, describing the effect of the Coulomb repulsion on the superconductivity, as well as possible electronic mechanisms for the superconductivity, are reviewed. The calculation of various properties within the Migdal-Eliashberg theory and attempts to go beyond this theory are described.

The theory and applications of wave self-focusing, collapse, and strongly nonlinear wave turbulence are reviewed. In the last decade, the theory of these phenomena and experimental realizations have progressed rapidly. Various nonlinear wave systems are discussed, but the simplest case of collapse and strong turbulence of Langmuir waves in an unmagnetized plasma is primarily used in explaining the theory and illustrating the main ideas. First, an overview of the basic physics of linear waves and nonlinear wave-wave interactions is given from an introductory perspective. Wave-wave processes are then considered in more detail. Next, an introductory overview of the physics of wave collapse and strong turbulence is provided, followed by a more detailed theoretical treatment. Later sections cover numerical simulations of Langmuir collapse and strong turbulence and experimental applications to space, ionospheric, and laboratory plasmas, including laser-plasma and beam-plasma interactions. Generalizations to self-focusing, collapse, and strong turbulence of waves in other systems are also discussed, including nonlinear optics, solid-state systems, magnetized auroral and astrophysical plasmas, and deep-water waves. The review ends with a summary of the main ideas of wave collapse and strong-turbulence theory, a collection of open questions in the field, and a brief discussion of possible future research directions.

Atmospheric turbulence profoundly limits the angular resolution of astronomical telescopes working at visible and near-infrared wavelengths. In fact, the angular resolution for conventional imaging through turbulence is on the order of 5–20t% of the diffraction-limited resolution at the best observatories in the world. The origin of these performance degradations is random turbulence-induced fluctuations in the index of refraction of the atmosphere. Random index-of-refraction fluctuations producing the optical path length of the atmosphere to be random in both space and time, producing random aberrations in the telescope pupil that degrade imaging performance. Over the past several years significant advances have been made in developing both hardware and image-processing-based techniques for improving the resolution of astronomical telescopes. Hardware-oriented correction techniques are based on wave-front sensing and adaptive optics. Image-processing-based methods include speckle-imaging techniques and hybrid imaging techniques that use elements of adaptive-optics systems and image reconstruction. Analysis techniques for predicting the performance of these imaging methods have been developed, and the comparative performance of these imaging techniques has been examined. This paper discusses turbulence and image-detection statistics, describes the fundamentals of methods for overcoming turbulence effects, and provides representative performance results.

The problem of determining the effects of the surrounding plasma on nuclear reaction rates in stars is formulated ab initio, using the techniques of quantum statistical mechanics. Subject to the condition that the nuclear reactions ensue only at very close approach of the fusing ions and the condition that the reaction be slow, the authors derive a result that expresses the complete effects of Coulomb barrier penetration and of the influence of the surrounding plasma in terms of matrix elements of well-defined operators. The corrections do not separate into the product of initial-state and final-state effects. When the energy release in the reaction is much greater than thermal energies, the corrections reduce, as expected, to evaluation of the equilibrium probability of one ion's being very near to the position of another ion. We address the calculation of this probability in an approach that is based on perturbation theory in the couplings of the plasma particles to the two fusing particles, with the Coulomb force between the fusing particles treated nonperturbatively and interactions among the plasma particles treated in the one-loop approximation. We recapture standard screening effects, find a correction term that depends on the quantum-mechanical nature of the plasma, and put an upper bound on the magnitude of the further correction terms for the case of a weakly coupled plasma. We find that possible ``dynamical screening'' effects that have been discussed in the literature are absent. The form of our results suggests that an approach that relies on numerical calculations of the correlation functions in a classical Coulomb gas, followed by construction of an effective two-body potential and a quantum barrier penetration calculation, will miss physics that is as important as the physics that it includes.

The authors review the relation between the inflationary potential and the spectra of density waves (scalar perturbations) and gravitational waves (tensor perturbations) produced, with particular emphasis on the possibility of reconstructing the inflaton potential from observations. The spectra provide a potentially powerful test of the inflationary hypothesis; they are not independent but instead are linked by consistency relations reflecting their origin from a single inflationary potential. To lowest order in a perturbation expansion there is a single, now familiar, relation between the tensor spectral index and the relative amplitude of the spectra. The authors demonstrate that there is an infinite hierarchy of such consistency equations, though observational difficulties suggest only the first is ever likely to be useful. They also note that since observations are expected to yield much better information on the scalars than on the tensors, it is likely to be the next-order version of this consistency equation that will be appropriate, not the lowest-order one. If inflation passes the consistency test, one can then confidently use the remaining observational information to constrain the inflationary potential, and the authors survey the general perturbative scheme for carrying out this procedure. Explicit expressions valid to next-lowest order in the expansion are presented. The prospects for future observations' reaching the quality required are then briefly assessed and simulated data sets motivated by this outlook are considered.

This paper outlines astrophysical issues related to the long-term fate of the universe. The authors consider the evolution of planets, stars, stellar populations, galaxies, and the universe itself over time scales that greatly exceed the current age of the universe. Their discussion starts with new stellar evolution calculations which follow the future evolution of the low-mass (M-type) stars that dominate the stellar mass function. They derive scaling relations that describe how the range of stellar masses and lifetimes depends on forthcoming increases in metallicity. They then proceed to determine the ultimate mass distribution of stellar remnants, i.e., the neutron stars, white dwarfs, and brown dwarfs remaining at the end of stellar evolution; this aggregate of remnants defines the 'final stellar mass function.' At times exceeding ∼1–10 trillion years, the supply of interstellar gas will be exhausted, yet star formation will continue at a highly attenuated level via collisions between brown dwarfs. This process tails off as the galaxy gradually depletes its stars by ejecting the majority and driving a minority toward eventual accretion onto massive black holes. As the galaxy disperses, stellar remnants provide a mechanism for converting the halo dark matter into radiative energy. Posited weakly interacting massive particles are accreted by white dwarfs, where they subsequently annihilate with each other. Thermalization of the decay products keeps the old white dwarfs much warmer than they would otherwise be. After accounting for the destruction of the galaxy, the authors consider the fate of the expelled degenerate objects (planets, white dwarfs, and neutron stars) within the explicit assumption that proton decay is a viable process. The evolution and eventual sublimation of these objects is dictated by the decay of their constituent nucleons, and this evolutionary scenario is developed in some detail. After white dwarfs and neutron stars have disappeared, galactic black holes slowly lose their mass as they emit Hawking radiation. This review finishes with an evaluation of cosmological issues that arise in connection with the long-term evolution of the universe. Special attention is devoted to the relation between future density fluctuations and the prospects for continued large-scale expansion. The authors compute the evolution of the background radiation fields of the universe. After several trillion years, the current cosmic microwave background will have redshifted into insignificance; the dominant contribution to the radiation background will arise from other sources, including stars, dark-matter annihilation, proton decay, and black holes. Finally, the authors consider the dramatic possible effects of a nonzero vacuum energy density.