Geophysical measurements of the gravitational constant and a recent reexamination of experiments performed early in the century on the equivalence of inertial and gravitational mass may have provided either observational clues to the unification of gravity with electroweak and strong nuclear forces or an indication of a new, previously unrecognized force. The evidence is still less than completely conclusive but it has now become difficult to find explanations of the geophysical observations other than non-Newtonian gravity. We also point to the requirements of the next generation of experiments. These include measurements of gravity or gravity gradient in the deep ocean and high above it and Von Eötvös-type experiments in steep terrain to test the possibility that a postulated short-range (100 to 1000 m) component of gravity depends upon fundamental particle count rather than mass.

This paper presents the results of a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment. It is primarily an extended account of results obtained over the last four years by the authors; while they try to provide some background for orientation, it is emphatically not intended as a comprehensive review of the literature on the subject. Its contents include (1) an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of a dissipative environment to the "spin-boson" problem; (2) the derivation of an exact formula for the dynamics of the latter problem; (3) the demonstration that there exists a simple approximation to this exact formula which is controlled, in the sense that we can put explicit bounds on the errors incurred in it, and that for almost all regions of the parameter space these errors are either very small in the limit of interest to us (the "slow-tunneling" limit) or can themselves be evaluated with satisfactory accuracy; (4) use of these results to obtain quantitative expressions for the dynamics of the system as a function of the spectral density $J\left(\omega \right)$ of its coupling to the environment. If $J\left(\omega \right)$ behaves as ${\omega }^s$ for frequencies of the order of the tunneling frequency or smaller, the authors find for the "unbiased" case the following results: For $s<\mathrm{}1\mathrm{}$ the system is localized at zero temperature, and at finite $T$ relaxes incoherently at a rate proportional to $\exp -{\left(\frac{T_0}{T}\right)}^{1-s}$. For $s>\mathrm{}2\mathrm{}$ it undergoes underdamped coherent oscillations for all relevant temperatures, while for $1<s<\mathrm{}2\mathrm{}$ there is a crossover from coherent oscillation to overdamped relaxation as $T$ increases. Exact expressions for the oscillation and/or relaxation rates are presented in all these cases. For the "ohmic" case, $s=1\mathrm{}$, the qualitative nature of the behavior depends critically on the dimensionless coupling strength $\alpha$ as well as the temperature $T$: over most of the ($\alpha$,$T$) plane (including the whole region $\alpha >1\mathrm{}$) the behavior is an incoherent relaxation at a rate proportional to $T^{2\alpha -1\mathrm{}}$, but for low $T$ and $0<\mathrm{}\alpha <\frac{1}{2}$ the authors predict a combination of damped coherent oscillation and incoherent background which appears to disagree with the results of all previous approximations. The case of finite bias is also discussed.

This review is an expository treatment of the displacement of one fluid by another in a two-dimensional geometry (a Hele-Shaw cell). The Saffman-Taylor equations modeling this system are discussed. They are simulated by random-walk techniques and studied by methods from complex analysis. The stability of the generated patterns (fingers) is studied by a WKB approximation and by complex analytic techniques. The primary conclusions reached are that (a) the fingers are linearly stable even at the highest velocities, (b) they are nonlinearly unstable against noise or an external perturbation, the critical amplitude for the noise being an exponential function of a power of the velocity for high velocities, (c) such exponentials seem to dominate high-velocity behavior, as can be seen from a WKB analysis, and (d) the results of the Saffman-Taylor equations disagree with experiments, apparently because they leave out film-flow phenomena.

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Neél model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

This paper is based on a series of eleven lectures that were presented at a workshop on The Physics of the Quark-Gluon Plasma held at Hua-Zhong Normal University in Wuhan, People's Republic of China, in September 1983. The lectures were updated for publication in November 1985. They cover perturbation theory of the plasma at high temperature, as well as the nonperturbative methods and results of lattice gauge theory computations. Physical models of the confinement-deconfinement phase transition and the modes of chiral symmetry breaking are presented. The possibility that a quark-gluon plasma might be produced in ultrarelativistic nuclear collisions is briefly discussed in the introductory lecture.

The preparation, or generation of coherent states, squeezed states, and photon number states is discussed. The quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadrature measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier. A quantum nondemolition measurement followed by a measurement of the conjugate variable is also categorized as a simultaneous measurement. It is shown that, for all of these schemes, the minimum uncertainty product of the measured variables is exactly equal to that required for a simultaneous measurement of two noncommuting variables. On the other hand, measurements of a single quadrature component are noise-free. Such measurements are degenerate heterodyning, degenerate parametric amplification, and cavity degenerate four-wave mixing and photon counting by a photomultiplier or avalanche photodiode. The Heisenberg uncertainty principle and the quantum-mechanical channel capacity of Shannon are discussed to address the question "How much information can be transmitted by a single photon?" The quantum-mechanical channel capacity provides an upper bound on the achievable information capacity and is ideally realized by photon number states and photon counting detection. Its value is $\frac{\hslash \omega }{\left(\ln 2\right)kT}$ bit per photon. The use of coherent or squeezed states and a simultaneous measurement of two quadrature field components or the measurement of one single quadrature field component does not achieve the ultimate limit.

Ultrametricity is a simple topological concept, but its appearance in the language of physicists is recent. This review provides all the elementary background (from mathematics, taxonomy, and statistical physics) and surveys the main fields of development (spin glasses, optimization theory). Static and dynamic aspects are covered. From present knowledge, one can already draw some tentative conclusions on the common causes for the occurrence of ultrametric structures in nature. Some perspectives on unresolved problems in physics and biology are also presented.

The theory of plasma relaxation is described and developed. Turbulence, allied with a small resistivity, allows the plasma rapid access to a particular minimum-energy state. This process involves reconnection of magnetic field lines in a manner that destroys all the topological invariants of ideal plasma so that only total magnetic helicity survives. Although this mechanism, and the equations describing the relaxed state, are similar in all systems, the properties of the relaxed state depend crucially on the topology—toroidal or spherical—of the container and on the boundary conditions. Consequently there are several different types of relaxed state, each with its own special characteristics, which are derived and discussed. The measurements made on many experiments, including toroidal pinches, OHTE, multipinch, and spheromaks, are reviewed and shown to be in striking agreement with the theoretical predictions.

This paper reviews the basic theory of the mechanical action of light in resonant interaction with atoms. At present the main application is laser cooling, but the approach is applicable to a broader range of phenomena. It is based on an adiabatic elimination philosophy, which turns out to give the lowest-order quantum corrections to the behavior found when the photon momentum goes to zero. Hence it is called a semiclassical theory. In this manner a subjective but consistent approach can be presented; other treatments are incorporated or mentioned at the appropriate places. Both the classical and the quantum-mechanical approach are discussed. Those readers who wish to obtain only a heuristic overview of the phenomena can concentrate on Sec. III, which treats both the photon momentum effects and their connection with photon counting statistics. The detailed theoretical treatment utilizes Wigner functions and Fokker-Planck techniques. The ensuing theory is applied both to the cooling of free particles and trapped ones. The paper ends with an extensive bibliography, where the author lists most papers of interest for research into the mechanical manifestations of light. For completeness, many papers are included that are not explicitly mentioned in the text.

The authors review the equations, notational choices, and confusing terminology of the Friedmann (zero-pressure) and Lemaître cosmological models, retaining cgs units as far as practical and in particular retaining units ${\mathrm{cm}}^{-2\mathrm{}}$ for the present Gaussian curvature $K_0$ of three-space. They integrate the Friedmann equation numerically, requiring solutions to match the present Hubble parameter $H_0$ and mass-density ("closure") parameter ${\Omega }_0$ at present time $t_0=0\mathrm{}$, and generate families of curves showing the scale factor $R\left(\tau \right)$ (with $R_0=1\mathrm{}$) vs $\tau$ (time in units $H_0^{-1\mathrm{}}$) for fixed ${\Omega }_0$ and various values of the cosmological constant $\Lambda$ (in units $H_0^2$). These unusual graphs show the continuity of the solutions and the physical significance of $\Lambda$. Families for several values of ${\Omega }_0$ exhibit known but unfamiliar features. The authors also show the family of "standard models" ($\Lambda =0\mathrm{}$) and the family satisfying the "inflationary constraint" ($K_0=0\mathrm{}$). They obtain new and simple formulas for the critical value ${\Lambda }_s(H_0,{\Omega }_0)$, which separates models with a big bang from those without. Their definition of ${\Lambda }_s$ at fixed $H_0$ and ${\Omega }_0$ differs from usual practice but proves useful. These formulas also give the quasistatic scale factor $R_s$ and redshift $z_s$ for the corresponding Eddington-Lemaître model, and give $R_s$ and $z_s$ approximately for the neighboring "Lemaître coasting models," which have $\Lambda <{\Lambda }_s$. The conventional wisdom that $\Lambda ={\Lambda }_c(1+\varepsilon )$ for the coasting models applies to a different characteristic value ${\Lambda }_c$. A quasistatic state in the future, with a second critical value ${\Lambda }_{s2}$, is possible if ${\Omega }_0>1\mathrm{}$. The parameters ${\Omega }_0$, $\frac{\Lambda }{H_0^2}$, $\frac{{\Lambda }_s}{H_0^2}$, and $\frac{{\Lambda }_{s2}}{H_0^2}$ can be used to classify the Friedmann models.

The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is relativistically invariant and fully causal. A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimente and "paradoxes." The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its "collapse." It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law ($P=\psi {\psi }^{*}$), basic elements of the Copenhagen interpretation.

The authors present an analysis of all extant data on isospin mixing in statistical compound-nucleus reactions. The analysis is based on a generalization of the Hauser-Feshbach formula allowing for isospin mixing. The strength of the mixing is described by a single parameter $z$. The theory is applicable when all compound-nucleus resonances overlap strongly. It is derived from a statistical theory of nuclear reactions allowing for the mixing of two classes of states. The parameter $z$ comprises both internal mixing (via the Coulomb interaction) and external mixing (via the channels). The theory contains both the static criterion (Coulomb matrix elements compared with spacings) and the dynamical criterion (spreading widths compared with decay widths) for isospin symmetry breaking. The theory yields the dependence on $z$ of observables like average cross sections, and auto- and cross-correlation functions. The data show that isospin symmetry breaking is neither so weak as to be altogether negligible, nor so strong as to reduce our theory to a Hauser-Feshbach formalism without any reference to the isospin quantum number. The authors argue in favor of a parametrization of isospin symmetry breaking in the data in terms of a spreading width rather than a Coulomb matrix element. They find that internal mixing dominates, and that the associated spreading width is nearly independent of mass number and excitation energy.

The subject of small metallic particle properties is outlined with emphasis on quantum electronic effects. The theoretical background for interpretation of experiments is discussed beginning with the work of Kubo. More recent amendments to this have been included, taking into account the techniques of random matrix theory and effects of the spin-orbit interaction. A general review of experimental work is presented in order to permit a comprehensive evaluation of current understanding of the quantum size effect on the electronic spectrum. This survey includes magnetic susceptibility, nuclear magnetic resonance, electron spin resonance, heat capacity, optical, and infrared absorption measurements. These are discussed in many instances from the point of view of there being competing size effects arising from a reduced volume contrasted with those from the surface. A number of stimulating and provocative results have led to the development of new areas of research involving metallic clusters such as cluster beam techniques, far-infrared absorption by particle clusters, adsorbate NMR, and particle-matrix composites. Although there is little question that the experiments themselves indicate the existence of quantum effects, there are as yet, insufficient results to test the theoretical predictions for electron-level distribution functions based on fundamental symmetries of the electron Hamiltonian. A new suggestion for measurement of the electron-level correlation function is made using the magnetic field dependence of the NMR Knight shift. Particle preparation methods are also reviewed with commentary on the problems and advantages of these techniques for investigation of quantum electronic effects.

The Shelter Island conference in 1947 was the stimulus for many of the important advances in quantum field theory following World War II. Schwinger, Feynman, Tomonaga, and Dyson were the principal contributors during the initial phase of these developments. This article attempts to reconstruct the genesis of Feynman's formulation of quantum electrodynamics, focusing principally on the period from 1947 to 1950.

Nuclear magnetic resonance in bulk matter was discovered independently by Purcell, Torrey, and Pound at Harvard and by Bloch, Hansen, and Packard at Stanford towards the end of 1945. Their experiments were so different that members of neither group were quick to recognize their own experiment in the other. The magnetic resonance phenomenon was conceptualized differently by the two groups, and the design of their experiments differed accordingly. The Purcell group thought of magnetic resonance in terms of transitions between quantum states while the Bloch group visualized magnetic moments being reoriented with respect to a magnetic field. The conceptual approach adopted by each group can be seen as a natural consequence of earlier influences.

This paper reviews the theory and applications of photoacoustic (also called optoacoustic) methods belonging to the more general area of photothermal measurement techniques. The theory covers excitation of gaseous or condensed samples with modulated continuous light beams or pulsed light beams. The applications of photoacoustic methods include spectroscopy, monitoring deexcitation processes, probing physical properties of materials, and generating mechanical motions. Several other related photothermal methods, as well as particle-acoustics and wave-acoustics methods are also described. This review complements an earlier and narrower review [Rev. Mod. Phys. 53, 517 (1981)] that is mainly concerned with sensitive detection by pulsed photoacoustic spectroscopy in condensed matter.

The author explores some of the inherent simplifications of "quantum lattice physics." He distinguishes between fermions and bosons and analyzes the $n$-body problem for each, with $n=1,2,3\mathrm{}\dots$ typically a small number. With delta-function (zero-range) interactions, the three-body problem on a lattice is manageable, and some results can even be extrapolated to $n\ge 4$. Such calculations are not limited to one dimension (where the well-known Bethe ansatz solves a number of $n$-body problems). On the contrary, studies cited are mainly in three dimensions and actually simplify with increasing dimensionality. For example, it is found that bound states of $n\ge 3$ particles in $d\ge 3$ dimensions are formed discontinuously as the strength of two-body attractive forces is increased, and are therefore always in the easily analyzed "strong coupling limit." In the Appendix, an exactly solved example from the theory of itinerant-electron magnetism illustrates how a rigorous solution to the few-body problem is capable of yielding information concerning the $N$-body problem.