The authors review the theory and phenomenology of instantons in quantum chromodynamics (QCD). After a general overview, they provide a pedagogical introduction to semiclassical methods in quantum mechanics and held theory. The main part of the review summarizes our understanding. of the instanton liquid in QCD and the role of instantons in generating the spectrum of light hadrons. The authors also discuss properties of instantons at finite temperature and how instantons can provide a mechanism for the chiral phase transition. They give an overview of the role of instantons in some other models, in particular low-dimensional sigma models, electroweak theory, and supersymmetric QCD.

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 isa 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.

Granular materials are ubiquitous in the world around us. They have properties that art different from those commonly associated with either solids, liquids, or gases. In this review the authors select some of the special properties of granular materials and describe recent research developments.

We review the present status of QCD corrections to weak decays beyond the leading-logarithmic approximation, including particle-antiparticle mixing and rare and CP-violating decays. After presenting the basic formalism for these calculations we discuss in detail the effective Hamiltonians of all decays for which the next-to-leading-order corrections are known. Subsequently, we present the phenomenological implications of these calculations. The values of various parameters are updated, in particular the mass of the newly discovered top quark. One of the central issues in this review are the theoretical uncertainties related to renormalization-scale ambiguities, which are substantially reduced by including next-to-leading-order corrections. The impact of this theoretical improvement on the determination of the Cabibbo-Kobayashi-Maskawa matrix is then illustrated.

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.

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 A(3)C(60) are not Mott-Hubbard insulators, in spite of the large Coulomb interaction. Estimates of the Coulomb pseudopotential mu*, 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.

A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite-temperature counterparts, their dynamic and static critical behaviors are intimately intertwined. Considerable insight is gained by considering the path-integral description of the quantum statistical mechanics of such systems, which takes the form of the classical statistical mechanics of a system in which time appears as an extra dimension. In particular, this allows the deduction of scaling forms for the finite-temperature behavior, which turns out to be described by the theory of finite-size scaling. It also leads naturally to the notion of a temperature-dependent dephasing length that governs the crossover between quantum and classical fluctuations. Using these ideas, a scaling analysis of experiments on Josephson-junction arrays and quantum-Hall-effect systems is presented.

Current technology is beginning to allow us to manipulate rather than just observe individual quantum phenomena. This opens up the possibility of exploiting quantum effects to perform computations beyond the scope of any classical computer. Recently Peter Shor discovered an efficient algorithm for factoring whole numbers, which uses characteristically quantum effects. The algorithm illustrates the potential power of quantum computation, as there is no known efficient classical method for solving this problem. The authors give an exposition of Shor's algorithm together with an introduction to quantum computation and complexity theory. They discuss experiments that may contribute to its practical implementation.

In the Born-Oppenheimer approximation for molecular dynamics as generalized by Born and Huang, nuclei move on multiple potential-energy surfaces corresponding to different electronic states. These surfaces may intersect at a point in the nuclear coordinates with the topology of a double cone. These conical intersections have important consequences for the dynamics. When an adiabatic electronic wave function is transported around a closed loop in nuclear coordinate space that encloses a conical intersection point, it acquires an additional geometric, or Berry, phase. The Schrodinger equation for nuclear motion must be modified accordingly. A conical intersection also permits efficient nonadiabatic transitions between potential-energy surfaces. Most examples of the geometric phase in molecular dynamics have been in situations in which a molecular point-group symmetry required the electronic degeneracy and the consequent conical intersection, Similarly, it has been commonly assumed that the conical intersections facilitating nonadiabatic transitions were largely symmetry driven. However, conical intersections also occur in the absence of any symmetry considerations. This review discusses computational tools for finding and characterizing the conical intersections in such systems. Because these purely accidental intersections are difficult to anticipate, they may occur more frequently than previously thought and in unexpected situations, making the geometric phase effect and the occurrence of efficient nonadiabatic transitions more commonplace phenomena.

We review experimental studies of the time decay of the nonequilibrium magnetization in high-temperature superconductors, a phenomenon known as magnetic relaxation. This effect has its origin in motion of flux lines out of their pinning sites due to thermal activation or quantum tunneling. The combination of relatively weak flux pinning and high temperatures leads to rich properties that are unconventional in the context of low temperature superconductivity and that have been the subject to intense studies. The results are assessed from a purely experimental perspective and discussed in the context of present phenomenological theories.

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 ate 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.

Multichannel atomic spectra frequently exhibit such extraordinary visual complexity that they appear at first glance to be uninterpretable. The present review discusses how to unravel such spectra through the use of theoretical multichannel spectroscopy to extract the key dynamical implications. Moreover, this class of techniques permits a quantitative prediction or reproduction of experimental spectra for some of the more challenging atomic systems under investigation. It is shown that multichannel spectroscopy marries the techniques of multichannel quantum-defect theory to the eigenchannel R-matrix method (or related methods). It has long been appreciated that multichannel quantum-defect theory can successfully use a collision-theory framework to interpret enormously complicated Rydberg spectra. However, the capabilities of multichannel quantum-defect theory have increased dramatically during the past decade, through the development of nearly ab initio methods for the calculation of the short-range scattering parameters that control the interactions of closed and open channels. In this review, emphasis is given to the alkaline-earth atoms, for which many different observables have been successfully compared with experiment over broad ranges of energy and resolution. Applications of the method to describe the photoionization spectra of more complex open-shell atoms are also discussed.

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 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.

This article reviews the dynamics and observational signatures of particles interacting with monopoles, beginning with a scholium in Newton's Principia. The orbits of particles in the field of a gravomagnetic monopole, the gravitational analog of a magnetic monopole, lie on cones; when the cones are slit open and flattened, the orbits are the ellipses and hyperbolas that one would have obtained without the gravomagnetic monopole. The more complex problem of a charged, spinning sphere in the held of a magnetic monopole is then discussed. The quantum-mechanical generalization of this latter problem is that of monopolar hydrogen. Previous work on monopolar hydrogen is reviewed and details of the predicted spectrum are given. Protons around uncharged monopoles have a bound continuum. Around charged ones, electrons have levels and decaying resonances, so magnetic monopoles can grow in mass by swallowing both electrons and protons. In general relativity, the spacetime produced by a gravomagnetic monopole is NUT space, named for Newman, Tamborino, and Unti (1963). This space has a nonspherical metric, even though a mass with a gravomagnetic monopole is spherically symmetric. All geodesics in NUT space lie on cones, and this result is used to discuss the gravitational lensing by bodies with gravomagnetic monopoles.

The current understanding of finite-temperature phase transitions in QCD is reviewed. A critical discussion of refined phase-transition criteria in numerical lattice simulations and of analytical tools going beyond the mean-field level in effective continuum models for QCD is presented. Theoretical predictions about the order of the transitions are compared with possible experimental manifestations in heavy-ion collisions. Various places in phenomenological descriptions are pointed out where more reliable data for QCD's equation of state would help in selecting the most realistic scenario among those proposed. Unanswered questions are raised about the relevance of calculations that assume thermodynamic equilibrium. Promising new approaches for implementing nonequilibrium aspects of the thermodynamics of heavy-ion collisions are described.

This article reviews the role of reparametrization invariance (the invariance of the properties of a system with respect to the choice of the co-ordinate system used to describe it) in deriving stochastic equations that describe the growth of surfaces. By imposing reparametrization invariance on a system, the authors identify the physical origin of many of the terms in its growth equations. Both continuum-growth equations for interfaces and equations for the coarse-grained evolution of discrete-lattice models are derived with this method. A detailed analysis of the discrete-lattice case and its small-gradient expansion provides a physical basis for terms found in commonly studied growth equations. The reparametrization-invariant formulation of growth processes also has the advantage of allowing one to model shadowing effects that are lost in the no-overhang approximation and to conserve underlying symmetries of the system that are lost in a small-gradient expansion. Finally, a knowledge of the full equation of motion, beyond the lowest-order gradient expansion, may be relevant in problems where the usual perturbative renormalization methods fail.

Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves el al., 1980, Rev. Mod. Phys. 52, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review.

The alkali-doped solid materials A(3)C(60) (where A is an alkali metal), which are superconductors with transition temperatures among the highest known apart from the high-T-c cuprates, are among the most exciting outgrowths of the discovery of the family of fullerene molecules. The structural, electronic, and superconducting properties of the alkali fullerides have been subjects of great controversy. In this article the authors review nuclear magnetic resonance (NMR) investigations of the alkali fullerides and of undoped C-60. They show that, although the NMR data certainly provide evidence for unusual static and dynamic structural properties, there is little evidence for unusual normal- and superconducting-state electronic properties, such as strong correlations in the normal state or nonphononic mechanisms of superconductivity.