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.

Recent progress concerning lattice dynamics in quasicrystals, both theoretical and experimental, is discussed. The theory deals with the general description, which differs from that for ordinary crystals, and with model calculations and rigorous results for one-, two-, and three-dimensional systems. Experimental results are restricted mainly to quasicrystals with icosahedral symmetry.

The problem of separating rotations from internal motions in systems such as macroscopic flexible bodies, atoms, molecules, nuclei, and solar systems is an old one, with many applications in physics, chemistry, and engineering. A new element, however, which has not been appreciated until fairly recently, is the existence of certain gauge fields on the reduced configuration space for such systems. These (non-Abelian) gauge fields arise in the ``falling cat'' problem, in which changes in shape induce changes in external orientation; but they also have a dynamical significance, and enter as gauge potentials in the Lagrangian or Hamiltonian describing the internal or reduced dynamics. Physically these gauge fields represent Coriolis effects. This review concentrates on the case of nonrelativistic, n-body systems not subject to external torques, and develops the gauge theory of rotations and internal motions in detail. Both classical and quantum treatments are given. The gauge theory is developed from the standpoint of classical, coordinate-based tensor analysis; more abstract mathematical notation is generally not used, although the basic geometrical ideas of fiber-bundle theory are developed as needed. Certain old results, such as the Wilson-Howard-Watson Hamiltonian of molecular physics, are examined from a gauge-theoretical standpoint; and several new results are presented, including field equations of the Kaluza-Klein type satisfied by the gauge fields, and geometrical interpretations of the Eckart frame.

Evidence for pair production of a new particle consistent with the standard-model top quark has been reported recently by groups studying proton-antiproton collisions at 1.8 TeV center-of-mass energy at the Fermi National Accelerator Laboratory. This paper both reviews the history of the search for the top quark in electron-positron and proton-antiproton collisions and reports on a number of precise electroweak measurements and the value of the top-quark mass that can be extracted from them. Within the context of the standard model, the authors review the theoretical predictions for top-quark production and the dominant backgrounds. They describe the collider and the detectors that were used to measure the pair-production process and the data from which the existence of the top quark is evinced. Finally, they suggest possible measurements that could be made in the future with more data, measurements that would confirm the nature of this particle, the details of its production in hadron collisions, and its decay properties.

This paper is a comprehensive review of almost twenty years of research on nuclear magnetic ordering, first in copper and later in silver and rhodium metals. The basic principles of nuclear magnetism and the measurement of positive and negative spin temperatures are discussed first. Cascade nuclear refrigeration techniques, susceptibility and nuclear-magnetic-resonance (NMR) measurements, and arrangements for neutron-diffraction experiments at nanokelvin and picokelvin temperatures are described next. Comprehensive magnetic-susceptibility and neutron-diffraction measurements on copper, which led to the discovery of at least three antiferromagnetic phases, one displaying the novel (0 ) spin structure and the other two showing the type-I order of the fcc system, are then described in detail. NMR data on silver, at T>0 and T<0, are presented next leading to the observation that silver orders antiferromagnetically at positive spin temperatures and ferromagnetically at negative spin temperatures. The authors discuss recent neutron-diffraction measurements that show that the antiferromagnetic structure at T>0 is in a single-k type-I state. NMR data on rhodium at T>0 and T<0 are also described. Results obtained on Tl, Sc, ${\mathrm{AuIn}}_2$, and metallic Pr compounds and on insulators like ${\mathrm{CaF}}_2$ are then discussed briefly. The paper is concluded by an extensive theoretical section. Calculations of conduction-electron mediated exchange interactions are described, and the mean-field theory of nuclear magnetic ordering is presented. The role of thermal and quantum fluctuations is then discussed, particularly in the selection of the antiferromagnetic ground state. Finally, theoretically calculated magnetic phase diagrams and ordered spin structures of copper and silver are presented in detail and compared with experimental results. The overall agreement is good, affirming the value of nuclear magnets in Cu and Ag as realizations of simple physical models.

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 Schrödinger 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. [S0034-6861(96)00404-7]

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. [S0034-6861(96)00104-3]

Granular materials are ubiquitous in the world around us. They have properties that are 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.[S0034-6861(96)00204-8]

The strong-coupling limit of a quantum system is in general quite complicated, but in some cases a great simplification occurs: the strongly coupled limit is equivalent to the weakly coupled limit of some other system. In string theory conjectures of this type go back several years, but only in the past year and a half has it been understood to be a general principle applying to all string theories. This has improved our understanding of string dynamics, including quantum gravity, in many new and sometimes surprising ways. The author describes these developments and puts them in the context of the search for the unified theory of particle physics and gravity. [S0034-6861(96)00604-6]

We review the present status of QCD corrections to weak decays beyond the leading-logarithmic approximation, including particle-antiparticle mixing and rare and $\mathrm{CP}$-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. [S0034-6861(96)00304-2]

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. [S0034-6861(96)00504-1]

Contrary to popular conception, the purpose of particle physics is to understand the everyday world. The current theory of fundamental interactions among the quarks and leptons depends on eighteen parameters, which are a priori arbitrary. Were these parameters different, our world would be changed dramatically. By exploring the connection between these parameters and everyday phenomena we can better appreciate the challenges confronting contemporary particle physics. Until we can explain the origin of these parameters, we cannot say we truly understand why our everyday world is as it is. [S0034-6861(96)00203-6]

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. [S0034-6861(96)00403-5]

The alkali-doped solid materials $A_3{\mathrm{C}}_{60}$ (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 ${\mathrm{C}}_{60}$. 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. [S0034-6861(96)00603-4]

The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]

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 et 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. [S0034-6861(96)00103-1]

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. [S0034-6861(96)00303-0]

Two ideas have greatly contributed to our understanding of baryon structure in the framework of quantum chromodynamics. The first, that of chiral symmetry, received its fundamental justification from QCD and has been developed into the powerful technique of chiral perturbation theory. The other notion is the large-$N_c$ limit, namely, the behavior of QCD in the limit where there are a large number of colors. Like chiral symmetry, the large-$N_c$ limit predicts many relations between baryon matrix elements. These so-called "model-independent" predictions should agree with each other, but paradoxically that is not always the case. The paradox is resolved by recognizing that the two limiting processes (the chiral and large-$N_c$ limits) do not commute. This noncommutativity can be traced to the special role played by the $\Delta$ resonance in large-$N_c$ QCD. This gives rise to a new parameter in the effective theory of baryons. [S0034-6861(96)00602-2]

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. [S0034-6861(96)00302-9]