Showing papers in "Reviews of Modern Physics in 1998"

Metal-insulator transitions

Abstract: Metal-insulator transitions are accompanied by huge resistivity changes, even over tens of orders of magnitude, and are widely observed in condensed-matter systems. This article presents the observations and current understanding of the metal-insulator transition with a pedagogical introduction to the subject. Especially important are the transitions driven by correlation effects associated with the electron-electron interaction. The insulating phase caused by the correlation effects is categorized as the Mott Insulator. Near the transition point the metallic state shows fluctuations and orderings in the spin, charge, and orbital degrees of freedom. The properties of these metals are frequently quite different from those of ordinary metals, as measured by transport, optical, and magnetic probes. The review first describes theoretical approaches to the unusual metallic states and to the metal-insulator transition. The Fermi-liquid theory treats the correlations that can be adiabatically connected with the noninteracting picture. Strong-coupling models that do not require Fermi-liquid behavior have also been developed. Much work has also been done on the scaling theory of the transition. A central issue for this review is the evaluation of these approaches in simple theoretical systems such as the Hubbard model and $t\ensuremath{-}J$ models. Another key issue is strong competition among various orderings as in the interplay of spin and orbital fluctuations. Experimentally, the unusual properties of the metallic state near the insulating transition have been most extensively studied in $d$-electron systems. In particular, there is revived interest in transition-metal oxides, motivated by the epoch-making findings of high-temperature superconductivity in cuprates and colossal magnetoresistance in manganites. The article reviews the rich phenomena of anomalous metallicity, taking as examples Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Ru compounds. The diverse phenomena include strong spin and orbital fluctuations, mass renormalization effects, incoherence of charge dynamics, and phase transitions under control of key parameters such as band filling, bandwidth, and dimensionality. These parameters are experimentally varied by doping, pressure, chemical composition, and magnetic fields. Much of the observed behavior can be described by the current theory. Open questions and future problems are also extracted from comparison between experimental results and theoretical achievements.

Instability, turbulence, and enhanced transport in accretion disks

Abstract: Recent years have witnessed dramatic progress in our understanding of how turbulence arises and transports angular momentum in astrophysical accretion disks. The key conceptual point has its origins in work dating from the 1950s, but its implications have been fully understood only in the last several years: the combination of a subthermal magnetic field (any nonpathological configuration will do) and outwardly decreasing differential rotation rapidly generates magnetohydrodynamic (MHD) turbulence via a remarkably simple linear instability. The result is a greatly enhanced effective viscosity, the origin of which had been a long-standing problem. The MHD nature of disk turbulence has linked two broad domains of magnetized fluid research: accretion theory and dynamos. The understanding that weak magnetic fields are not merely passively acted upon by turbulence, but actively generate it, means that the assumptions of classical dynamo theory break down in disks. Paralleling the new conceptual understanding has been the development of powerful numerical MHD codes. These have taught us that disks truly are turbulent, transporting angular momentum at greatly enhanced rates. We have also learned, however, that not all forms of disk turbulence do this. Purely hydrodynamic turbulence, when it is imposed, simply causes fluctuations without a significant increase in transport. The interplay between numerical simulation and analytic arguments has been particularly fruitful in accretion disk theory and is a major focus of this article. The authors conclude with a summary of what is now known of disk turbulence and mention some knotty outstanding questions (e.g., what is the physics behind nonlinear field saturation?) for which we may soon begin to develop answers.

Coherent population transfer among quantum states of atoms and molecules

Abstract: The authors discuss the technique of stimulated Raman adiabatic passage (STIRAP), a method of using partially overlapping pulses (from pump and Stokes lasers) to produce complete population transfer between two quantum states of an atom or molecule. The procedure relies on the initial creation of a coherence (a population-trapping state) with subsequent adiabatic evolution. The authors present the basic theory, with some extensions, and then describe examples of experimental utilization. They note some applications of the technique not only to preparation of selected states for reaction studies, but also to quantum optics and atom optics.

The quantum-jump approach to dissipative dynamics in quantum optics

Abstract: Dissipation, the irreversible loss of energy and coherence, from a microsystem is the result of coupling to a much larger macrosystem (or reservoir) that is so large that one has no chance of keeping track of all of its degrees of freedom. The microsystem evolution is then described by tracing over the reservoir states, which results in an irreversible decay as excitation leaks out of the initially excited microsystems into the outer reservoir environment. Earlier treatments of this dissipation used density matrices to describe an ensemble of microsystems, either in the Schr\"odinger picture with master equations, or in the Heisenberg picture with Langevin equations. The development of experimental techniques to study single quantum systems (for example, single trapped ions, or cavity-radiation-field modes) has stimulated the construction of theoretical methods to describe individual realizations conditioned on a particular observation record of the decay channel. These methods, variously described as quantum-jump, Monte Carlo wave function, and quantum-trajectory methods, are the subject of this review article. We discuss their derivation, apply them to a number of current problems in quantum optics, and relate them to ensemble descriptions.

Instantons in QCD

Abstract: 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 field 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.

Black Holes

Abstract: Black holes are among the most intriguing objects in modern physics Their influence ranges from powering quasars and other active galactic nuclei, to providing key insights into quantum gravity We review the observational evidence for black holes, and briefly discuss some of their properties We also describe some recent developments involving cosmic censorship and the statistical origin of black hole entropy

Hamiltonian description of the ideal fluid

Abstract: The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable whenmore » nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. {copyright} {ital 1998} {ital The American Physical Society}« less

Magnetic, transport, and optical properties of monolayer copper oxides

Abstract: The authors review the results of a wide variety of experiments on materials such as ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}$ that contain weakly coupled ${\mathrm{CuO}}_{2}$ layers. These materials are antiferromagnetic insulators with very large Heisenberg exchange energies, which become high-temperature superconductors when charge carriers are added to the ${\mathrm{CuO}}_{2}$ layers. The growth of large single crystals has made it possible to carry out neutron scattering, as well as anisotropic optical, transport, and magnetization measurements. The properties of the undoped ${\mathrm{CuO}}_{2}$ layer are reviewed, and the evolution of magnetic, optical, and transport properties with the addition of charge carriers is discussed. The emphasis is on the pure and lightly doped materials, although the magnetism in the superconductors is discussed.

Renormalization group theory: Its basis and formulation in statistical physics

Abstract: The nature and origins of renormalization group ideas in statistical physics and condensed matter theory are recounted informally, emphasizing those features of prime importance in these areas of science in contradistinction to quantum field theory, in particular: critical exponents and scaling, relevance, irrelevance and marginality, universality, and Wilson's crucial concept of flows and fixed points in a large space of Hamiltonians.

Solar fusion cross sections

Abstract: We review and analyze the available information on the nuclear-fusion cross sections that are most important for solar energy generation and solar neutrino production. We provide best values for the low-energy cross-section factors and, wherever possible, estimates of the uncertainties. We also describe the most important experiments and calculations that are required in order to improve our knowledge of solar fusion rates.

Electroweak Baryogenesis

Abstract: Contrary to naive cosmological expectations, all evidence suggests that the universe contains an abundance of matter over antimatter This article reviews the currently popular scenario in which testable physics, present in the standard model of electroweak interactions and its modest extensions, is responsible for this fundamental cosmological datum A pedagogical explanation of the motivations and physics behind electroweak baryogenesis is provided, and analytical approaches, numerical studies, up to date developments and open questions in the field are also discussed

Quantum tunneling in nuclear fusion

Abstract: Recent theoretical advances in the study of heavy-ion fusion reactions below the Coulomb barrier are reviewed. Particular emphasis is given to new ways of analyzing data (such as studying barrier distributions), new approaches to channel coupling (such as the path-integral and Green's function formalisms), and alternative methods to describe nuclear structure effects (such as those using the interacting boson model). The roles of nucleon transfer, asymmetry effects, higher-order couplings, and shape phase transitions are elucidated. The current status of the fusion of unstable nuclei and very massive systems are briefly discussed.

Structure and dynamics of few-nucleon systems

Abstract: Few-nucleon physics is a field rich with high-quality experimental data and possibilities for accurate calculations of strongly correlated quantum systems. In this article the authors discuss the traditional model of the nucleus as a system of interacting nucleons and outline many recent experimental results and theoretical developments in the field of few-nucleon physics. The authors describe nuclear structure and spectra, clustering and correlations, elastic and inelastic electromagnetic form factors, low-energy electroweak reactions, and nuclear scattering and response in the quasielastic regime. Through a review of the rich body of experimental data and a variety of theoretical developments, a coherent description of the nuclear strong- and electroweak-interaction properties emerges. In this article, the authors attempt to provide some insight into the practice and possibilities in few-nucleon physics today.

Astrometry and geodesy with radio interferometry: experiments, models, results

Abstract: Interferometry at radio frequencies between Earth-based receivers separated by intercontinental distances has made significant contributions to astrometry and geophysics during the past three decades. Analyses of such very long baseline interferometric (VLBI) experiments now permit measurements of relative positions of points on the Earth's surface and of angles between celestial objects at levels of better than one cm and one nanoradian, respectively. The relative angular positions of extragalactic radio sources inferred from this technique presently form the best realization of an inertial reference frame. This review summarizes the current status of radio interferometric measurements for astrometric and geodetic applications. It emphasizes the theoretical models that are required to extract results from the VLBI observables at present accuracy levels. An unusually broad cross section of physics contributes to the required modeling. Both special and general relativity need to be considered in properly formulating the geometric part of the propagation delay. While high-altitude atmospheric charged-particle (ionospheric) effects are easily calibrated for measurements employing two well-separated frequencies, the contribution of the neutral atmosphere at lower altitudes is more difficult to remove. In fact, mismodeling of the troposphere remains the dominant error source. Plate tectonic motions of the observing stations need to be taken into account, as well as the nonpointlike intensity distributions of many sources. Numerous small periodic and quasiperiodic tidal effects also make important contributions to space geodetic observables at the centimeter level, and some of these are just beginning to be characterized. Another area of current rapid advances is the specification of the orientation of the Earth's spin axis in inertial space: nutation and precession. Highlights of the achievements of very long baseline interferometry are presented in four areas: reference frames, Earth orientation, atmospheric effects on microwave propagation, and relativity. The order-of-magnitude improvement of accuracy that was achieved during the last decade has provided essential input to geophysical models of the Earth's internal structure. Most aspects of VLBI modeling are also directly applicable to interpretation of other space geodetic measurements, such as active and passive ranging to Earth-orbiting satellites, interplanetary spacecraft, and the Moon.

Big-bang nucleosynthesis enters the precision era

Abstract: The last parameter of big-bang nucleosynthesis, the baryon density, is being pinned down by measurements of the deuterium abundance in high-redshift hydrogen clouds. When it is determined, it will

Quasinormal-mode expansion for waves in open systems

Abstract: An open system is not conservative because energy can escape to the outside. As a result, the time-evolution operator is not Hermitian in the usual sense and the eigenfunctions (factorized solutions in space and time) are no longer normal modes but quasinormal modes (QNMs) whose frequencies $\ensuremath{\omega}$ are complex. Qausinormal-mode analysis has been a powerful tool for investigating open systems. Previous studies have been mostly system specific, and use a few QNMs to provide approximate descriptions. Here the authors review developments that lead to a unifying treatment. The formulation leads to a mathematical structure in close analogy to that in conservative, Hermitian systems. Hence many of the mathematical tools for the latter can be transcribed. Emphasis is placed on those cases in which the QNMs form a complete set and thus give an exact description of the dynamics. In situations where the QNMs are not complete, the ``remainder'' is characterized. Applications to optics in microspheres and to gravitational waves from black holes are given as examples. The second-quantized theory is sketched. Directions for further development are outlined.

Topological analysis of chaotic dynamical systems

Abstract: Topological methods have recently been developed for the analysis of dissipative dynamical systems that operate in the chaotic regime. They were originally developed for three-dimensional dissipative dynamical systems, but they are applicable to all ‘‘low-dimensional’’ dynamical systems. These are systems for which the flow rapidly relaxes to a three-dimensional subspace of phase space. Equivalently, the associated attractor has Lyapunov dimension d L,3. Topological methods supplement methods previously developed to determine the values of metric and dynamical invariants. However, topological methods possess three additional features: they describe how to model the dynamics; they allow validation of the models so developed; and the topological invariants are robust under changes in control-parameter values. The topological-analysis procedure depends on identifying the stretching and squeezing mechanisms that act to create a strange attractor and organize all the unstable periodic orbits in this attractor in a unique way. The stretching and squeezing mechanisms are represented by a caricature, a branched manifold, which is also called a template or a knot holder. This turns out to be a version of the dynamical system in the limit of infinite dissipation. This topological structure is identified by a set of integer invariants. One of the truly remarkable results of the topological-analysis procedure is that these integer invariants can be extracted from a chaotic time series. Furthermore, self-consistency checks can be used to confirm the integer values. These integers can be used to determine whether or not two dynamical systems are equivalent; in particular, they can determine whether a model developed from time-series data is an accurate representation of a physical system. Conversely, these integers can be used to provide a model for the dynamical mechanisms that generate chaotic data. In fact, the author has constructed a doubly discrete classification of strange attractors. The underlying branched manifold provides one discrete classification. Each branched manifold has an ‘‘unfolding’’ or perturbation in which some subset of orbits is removed. The remaining orbits are determined by a basis set of orbits that forces the presence of all remaining orbits. Branched manifolds and basis sets of orbits provide this doubly discrete classification of strange attractors. In this review the author describes the steps that have been developed to implement the topological-analysis procedure. In addition, the author illustrates how to apply this procedure by carrying out the analysis of several experimental data sets. The results obtained for several other experimental time series that exhibit chaotic behavior are also described. [S0034-6861(98)00304-3]

Point scatterers for classical waves

Abstract: The authors present a closed formulation of resonant point scatterers for classical-wave propagation problems. A Green’s-function approach is employed in which all the small-distance singularities are regularized. Application of point scatterers considerably simplifies multiple-scattering calculations needed, for instance, for understanding the optical properties of dense cold gases and optical lattices. In the case of the vector description of light, it is shown that two different regularization parameters are required in order to obtain physically meaningful results. One parameter is related to the physical size of the pointlike scattering particle, while the other is connected to its dynamic properties. All parameters involved are defined in terms of physical observables leading to a complete and self-consistent treatment. The applicability of the point-scatterer model to several physical models is demonstrated. We calculate the local density of states of waves in the presence of one resonant point scatterer. For the vector case, the bare polarizability is shown to enter the local density of states. For a collection of resonant point dipoles, the Lorentz-Lorenz relation for the dielectric constant is derived for cubic lattices and for disordered arrangements. [S0034-6861(98)00302-X]

Application of superconducting quantum interference devices to nuclear magnetic resonance

Abstract: Nuclear magnetic resonance (NMR) provides information in low polarizing fields that is hard to obtain in high fields. A new generation of sensitive NMR detectors, the superconducting quantum interference device (SQUID), provides a fresh approach to low-field NMR studies. The SQUID is an ideal detector for low-field NMR, since its response does not depend on signal frequency as is the case of conventional NMR spectrometers. This review describes the experimental and theoretical studies in which SQUIDs have been used for the detection of NMR. Particular attention is paid to the calculation of the signal-to-noise ratio of SQUID NMR spectrometers with various input configurations as compared to that of conventional ones. The application of SQUIDs to nuclear thermometry and to absolute field measurements are also discussed. A SQUID directly measures the longitudinal nuclear magnetization ${M}_{z}$ and the review discusses extensively what we call ${M}_{z}$ spectroscopy.

Single-photon detection by rod cells of the retina

Abstract: At low light levels, the visual system detects and counts photon absorptions with a reliability close to limits set by statistical fluctuations in the number of absorbed photons. Thus the rod photoreceptors that provide the input signals to the dark-adapted visual system act as nearly perfect photon counters. This elegant performance is possible because light detection in the rods satisfies four functional requirements: high quantum efficiency, sufficient amplification to produce a measurable response, low dark noise, and low trial-to-trial variability in the elementary response. The rod meets these requirements using biochemical reactions rather than the solid-state reactions of silicon detectors, yet its performance equals or exceeds that of man-made detectors in several ways.

Classical monopoles: Newton, NUT space, gravomagnetic lensing, and atomic spectra

Abstract: This article reviews the dynamics and observational signatures of particles interacting with monopoles, beginning with a scholium in Newton'sPrincipia. 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 field 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.

Nonlinear optics of semiconductor and molecular nanostructures; a common perspective

Abstract: A unified microscopic theoretical framework for the calculation of optical excitations in molecular and semiconductor materials is presented. The hierarchy of many-body density matrices for a pair-conserving many-electron model and the Frenkel exciton model is rigorously truncated to a given order in the radiation field. Closed equations of motion are derived for five generating functions representing the dynamics up to third order in the laser field including phonon degrees of freedom as well as all direct and exchange-type contributions to the Coulomb interaction. By eliminating the phonons perturbatively the authors obtain equations that, in the case of the many-electron system, generalize the semiconductor Bloch equations, are particularly suited for the analysis of the interplay between coherent and incoherent dynamics including many-body correlations, and lead to thermalized exciton (rather than single-particle) distributions at long times. A complete structural equivalence with the Frenkel exciton model of molecular materials is established. [S0034-6861(98)00201-3]

Proton-antiproton annihilation and meson spectroscopy with the Crystal Barrel

Abstract: This report reviews the achievements of the Crystal Barrel experiment at the Low Energy Antiproton Ring (LEAR) at CERN. During seven years of operation Crystal Barrel has collected very large statistical samples in pbarp annihilation, especially at rest and with emphasis on final states with high neutral multiplicity. The measured rates for annihilation into various two-body channels and for electromagnetic processes have been used to test simple models for the annihilation mechanism based on the quark internal structure of hadrons. From three-body annihilations three scalar mesons, a0(1450), f0(1370) and f0(1500) have been established in various decay modes. One of them, f0(1500), may be identified with the expected ground state scalar glueball.

Moon-Earth-Sun: The oldest three-body problem

Abstract: The daily motion of the Moon through the sky has many unusual features that a careful observer can discover without the help of instruments. The three different frequencies for the three degrees of freedom have been known very accurately for 3000 years, and the geometric explanation of the Greek astronomers was basically correct. Whereas Kepler's laws are sufficient for describing the motion of the planets around the Sun, even the most obvious facts about the lunar motion cannot be understood without the gravitational attraction of both the Earth and the Sun. Newton discussed this problem at great length, and with mixed success; it was the only testing ground for his Universal Gravitation. This background for today's many-body theory is discussed in some detail because all the guiding principles for our understanding can be traced to the earliest developments of astronomy. They are the oldest results of scientific inquiry, and they were the first ones to be confirmed by the great physicist-mathematicians of the 18th century. By a variety of methods, Laplace was able to claim complete agreement of celestial mechanics with the astronomical observations. Lagrange initiated a new trend wherein the mathematical problems of mechanics could all be solved by the same uniform process; canonical transformations eventually won the field. They were used for the first time on a large scale by Delaunay to find the ultimate solution of the lunar problem by perturbing the solution of the two-body Earth-Moon problem. Hill then treated the lunar trajectory as a displacement from a periodic orbit that is an exact solution of a restricted three-body problem. Newton's difficultly in explaining the motion of the lunar perigee was finally resolved, and the Moon's orbit was computed by a new method that became the universal standard until after WW II. Poincar\'e opened the 20th century with his analysis of trajectories in phase space, his insistence on investigating periodic orbits even in ergodic systems, and his critique of perturbation theory, particularly in the case of the Moon's motion. Space exploration, astrophysics, and the landing of the astronauts on the Moon led to a new flowering of celestial mechanics. Lunar theory now has to confront many new data beyond the simple three-body problem in order to improve its accuracy below the precision of 1 arcsecond; the computer dominates all the theoretical advances. This review is intended as a case study of the many stages that characterize the slow development of a problem in physics from simple observations through many forms of explanation to a high-precision fit with the data.

Precision measurements with high-energy neutrino beams

Abstract: Neutrino-scattering measurements offer a unique tool for probing the electroweak and strong interactions as described by the standard model. Electroweak measurements are accessible through the comparison of neutrino neutral- and charged-current scattering. These measurements are complementary to other electroweak measurements due to differences in the radiative corrections both within and outside the standard model. Neutrino-scattering measurements also provide a precise method for measuring the ${F}_{2}{(x,Q}^{2})$ and ${\mathrm{xF}}_{3}{(x,Q}^{2})$ structure functions. The predicted ${\mathrm{Q}}^{2}$ evolution can be used to test perturbative quantum chromodynamics as well as to measure the strong-coupling constant ${\ensuremath{\alpha}}_{s}$ and the valence, sea, and gluon parton distributions. In addition, neutrino charm production, which can be determined from the observed dimuon events, allows the strange-quark sea to be investigated along with measurements of the CKM matrix element $|{V}_{\mathrm{cd}}|$ and the charm quark mass.

Natural patterns and wavelets

Abstract: An introductory review of pattern formation in extended dissipative systems is presented. Examples from many areas of physics are introduced, and the mathematical analysis of the patterns formed by these systems is outlined, for patterns near and far from onset. The wavelet transform is introduced as a useful tool for the extraction of order parameters from patterns.