Showing papers in "Reviews of Modern Physics in 1989"

The Cosmological Constant Problem

Abstract: Astronomical observations indicate that the cosmological constant is many orders of magnitude smaller than estimated in modern theories of elementary particles. After a brief review of the history of this problem, five different approaches to its solution are described.

The density functional formalism, its applications and prospects

Abstract: A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.

Thermal boundary resistance

Abstract: The thermal boundary resistance present at interfaces between helium and solids (Kapitza resistance) and the thermal boundary resistance at interfaces between two solids are discussed for temperatures above 0.1 K. The apparent qualitative differences in the behavior of the boundary resistance at these two types of interfaces can be understood within the context of two limiting models of the boundary resistance, the acoustic mismatch model, which assumes no scattering, and the diffuse mismatch model, which assumes that all phonons incident on the interface will scatter. If the acoustic impedances of the two media in contact are very different, as is the case for helium (liquid or solid) in contact with a solid, then phonon scattering at the interface will reduce the boundary resistance. In the limiting case of diffuse mismatch, this reduction is typically over 2 orders of magnitude. Phonons are very sensitive to surface defects, and therefore the Kapitza resistance is very sensitive to the condition of the interface. For typical solid-solid interfaces, at which the acoustic impedances are less different, the influence of diffuse scattering is relatively small; even for the two limiting cases of acoustic mismatch and diffuse mismatch the predicted boundary resistances differ by very little (\ensuremath{\lesssim} 30%). Consequently, the experimentally determined values are expected to be rather insensitive to the condition of the interface, in agreement with recent observations. Subsurface (bulk) disorder and imperfect physical contact between the solids play far more important roles and led to the irreproducibilities observed in the early measurements of the solid-solid thermal boundary resistance.

Dynamics of Solitons in Nearly Integrable Systems

Abstract: A detailed survey of the technique of perturbation theory for nearly integrable systems, based upon the inverse scattering transform, and a minute account of results obtained by means of that technique and alternative methods are given. Attention is focused on four classical nonlinear equations: the Korteweg-de Vries, nonlinear Schr\"odinger, sine-Gordon, and Landau-Lifshitz equations perturbed by various Hamiltonian and/or dissipative terms; a comprehensive list of physical applications of these perturbed equations is compiled. Systems of weakly coupled equations, which become exactly integrable when decoupled, are also considered in detail. Adiabatic and radiative effects in dynamics of one and several solitons (both simple and compound) are analyzed. Generalizations of the perturbation theory to quasi-one-dimensional and quantum (semiclassical) solitons, as well as to nonsoliton nonlinear wave packets, are also considered.

Point defects and dopant diffusion in silicon

Abstract: Diffusion in silicon of elements from columns III and V of the Periodic Table is reviewed in theory and experiment. The emphasis is on the interactions of these substitutional dopants with point defects (vacancies and interstitials) as part of their diffusion mechanisms. The goal of this paper is to unify available experimental observations within the framework of a set of physical models that can be utilized in computer simulations to predict diffusion processes in silicon. The authors assess the present state of experimental data for basic parameters such as point-defect diffusivities and equilibrium concentrations and address a number of questions regarding the mechanisms of dopant diffusion. They offer illustrative examples of ways that diffusion may be modeled in one and two dimensions by solving continuity equations for point defects and dopants. Outstanding questions and inadequacies in existing formulations are identified by comparing computer simulations with experimental results. A summary of the progress made in this field in recent years and of directions future research may take is presented.

Electronic structure of the high-temperature oxide superconductors

Abstract: Since the discovery of superconductivity above 30 K by Bednorz and M\"uller in the La copper oxide system, the critical temperature has been raised to 90 K in Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and to 110 and 125 K in Bi-based and Tl-based copper oxides, respectively. In the two years since this Nobel-prize-winning discovery, a large number of electronic structure calculations have been carried out as a first step in understanding the electronic properties of these materials. In this paper these calculations (mostly of the density-functional type) are gathered and reviewed, and their results are compared with the relevant experimental data. The picture that emerges is one in which the important electronic states are dominated by the copper $d$ and oxygen $p$ orbitals, with strong hybridization between them. Photon, electron, and positron spectroscopies provide important information about the electronic states, and comparison with electronic structure calculations indicates that, while many features can be interpreted in terms of existing calculations, self-energy corrections ("correlations") are important for a more detailed understanding. The antiferromagnetism that occurs in some regions of the phase diagram poses a particularly challenging problem for any detailed theory. The study of structural stability, lattice dynamics, and electron-phonon coupling in the copper oxides is also discussed. Finally, a brief review is given of the attempts so far to identify interaction constants appropriate for a model Hamiltonian treatment of many-body interactions in these materials.

Tunneling times: a critical review

Abstract: The old question of "How long does it take to tunnel through a barrier?" has acquired new urgency with the advent of techniques for the fabrication of semiconductor structures in the nanometer range. For the restricted problem of tunneling in a scattering configuration, a coherent picture is now emerging. The dwell time ${\ensuremath{\tau}}_{D}$ has the status of an exact statement of the time spent in a region of space, averaged over all incoming particles. The phase times ${\ensuremath{\tau}}_{T}^{\ensuremath{\phi}}$ and ${\ensuremath{\tau}}_{R}^{\ensuremath{\phi}}$ are defined separately for transmitted and reflected particles. They are asymptotic statements on completed scattering events and include self-interference delays as well as the time spent in the barrier. Consequently, neither the dwell time nor the phase times can answer the question of how much time a transmitted (alternatively, reflected) particle spent in the barrier region. Our discussion of this question relies on a few simple criteria: (1) The average duration of a physical process must be real. (2) Since transmission and reflection are mutually exclusive events, the times ${\ensuremath{\tau}}_{T}$ and ${\ensuremath{\tau}}_{R}$ spent in the barrier region are, if they exist, conditional averages. Consequently, they must obey the identity ${\ensuremath{\tau}}_{D}=T{\ensuremath{\tau}}_{T}+R{\ensuremath{\tau}}_{R}$, where $T$ and $R$ are the transmission and reflection probabilities, respectively. The existence of this identity distinguishes tunneling in a scattering configuration from tunneling out of a metastable state. (3) Any proposed ${\ensuremath{\tau}}_{T}$ and ${\ensuremath{\tau}}_{R}$ must meet every requirement that can be constructed from ${\ensuremath{\tau}}_{D}$. On the basis of (2), the naively extrapolated phase times, as well as the B\"uttiker-Landauer time, must be rejected. The local Larmor times, as introduced by Baz', satisfy (2), but not every criterion of type (3). The local Larmor clock is therefore unreliable. The asymptotic Larmor clock shows the phase times, as it should. Finally, the inverse characteristic frequency of an oscillating barrier cannot always be defined. It is shown not to represent the duration of the tunneling process. This leaves the dwell time and the phase times as the only well-established times in this context. It also leaves open the question of the length of time a transmitted particle spends in the barrier region. It is not clear that a generally valid answer to this question exists.

The large-scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium

Abstract: The density distribution arising at the nonlinear stage of gravitational instability is similar to intermittency phenomena in acoustic turbulence. Initially small-amplitude density fluctuations of Gaussian type transform into thin dense pancakes, filaments, and compact clumps of matter. It is perhaps surprising that the motion of self-gravitating matter in the expanding universe is like that of noninteracting matter moving by inertia. A similar process is the distribution of light reflected or refracted from rippled water. The similarity of gravitational instability to acoustic turbulence is highlighted by the fact that late nonlinear stages of density perturbation growth can be described by the Burgers equation, which is well known in the theory of turbulence. The phenomena discussed in this article are closely related to the problem of the formation of large-scale structure of the universe, which is also discussed.

The Riemann problem for fluid flow of real materials

Abstract: The Riemann problem for fluid flow of real materials is examined. An arbitrary equation of state is allowed, subject only to the physical requirements of thermodynamics. The properties of the isentropes and the shock Hugoniot loci that follow from conditions imposed on the equation of state are reviewed systematically. Important properties of these wave curves are determined by three dimensionless variables characterizing the equation of state: the adiabatic exponent $\ensuremath{\gamma}$, the Gr\"uneisen coefficient $\ensuremath{\Gamma}$, and the fundamental derivative $\mathcal{G}$. Standard assumptions on these variables break down near phase transitions. The result is an anomalous wave structure: either shock waves split into multiple waves, or composite waves form. Additional questions related to shock stability and nonuniqueness of the solution of the Riemann problem are discussed.

Neutrino Oscillations in Matter

Abstract: Nonzero neutrino masses would provide new, unique information on particle physics beyond the standard model. Neutrino flavor oscillations provide the most sensitive method for directly testing for small neutrino masses. When the oscillations occur in matter, a resonance can occur that dramatically enhances the flavor mixing and can lead to conversion from one neutrino flavor to another. This is an attractive solution to the long-standing "solar neutrino problem." The phenomenon of neutrino oscillations in matter is reviewed. Analytic descriptions of the neutrino flavor survival probability in matter are considered in detail. A discussion is given for applications of neutrino oscillations in matter for the sun, Earth, supernovae, and the early universe.

Crystalline liquids: the blue phases

Abstract: The blue phases of cholesteric liquid crystals are liquids that exhibit orientational order characterized by crystallographic space-group symmetries. We present here a pedagogical introduction to the current understanding of the equilibrium structure of these phases accompanied by a general overview of major experimental results. Using the Ginzburg-Landau free energy appropriate to the system, we first discuss in detail the character and stability of the usual helical phase of cholesterics, showing that for certain parameter ranges the helical phase is unstable to the appearance of one or more blue phases. The two principal models for the blue phases are two limiting cases of the Ginzburg-Landau theory. We explore each limit and conclude with some general considerations of defects in both models and an exact minimization of the free energy in a curved three-dimensional space.

Introduction to bifurcation theory

Abstract: The theory of bifurcation from equilibria based on center-manifold reduction and Poincar\'e-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail: a Hopf bifurcation occurring in a model of three-wave mode coupling and steady-state bifurcations occurring in the real Landau-Ginzburg equation. The former provides an example of the importance of degenerate bifurcations in problems with more than one parameter and the latter illustrates new effects introduced into a bifurcation problem by a continuous symmetry.

The analytical representation of electronic potential-energy surfaces

Abstract: This article reviews the commonly used methods for representing electronic potential-energy surfaces for small molecules and simple chemical reactions in terms of globally defined analytical functions. Four classes of methods are discussed: spline fitting methods, semiempirical methods, many-body expansion methods, and methods that represent global surfaces based on information determined along reaction paths. The application of these methods is examined in detail for four triatomic systems and one four-atom system: $\mathrm{O}(^{3}P)+{\mathrm{H}}_{2}$, Cl+HCl, H+CO, $\mathrm{O}(^{1}D)+{\mathrm{H}}_{2}\ensuremath{\rightarrow}{\mathrm{H}}_{2}\mathrm{O}\ensuremath{\rightarrow}\mathrm{OH}+\mathrm{H}$, and H+C${\mathrm{O}}_{2}$\ensuremath{\rightarrow}OH+CO. These examples illustrate both the art and the pitfalls of representing surfaces. In addition, the consequences of different potential surface representations for the dynamics of collisions on these surfaces are discussed at length.

The dynamic origin of increasing entropy

Abstract: Thermodynamic states are assumed to be characterized by densities. Recent ergodic-theory results on the evolution of densities are used to give a unified treatment of the origin of classical nonequilibrium thermodynamic behavior. Asymptotic periodicity is sufficient for the existence of at least one state of (metastable) thermodynamic equilibrium and for the evolution of the entropy to a relative maximum that depends on the way the system is prepared. Ergodicity is necessary and sufficient for a unique state of thermodynamic equilibrium to exist. Exactness, a property of chaotic semidynamical (irreversible) systems, is necessary and sufficient for the global evolution of the entropy to its unique maximum for all initial states. Since all of the laws of physics are formulated as (reversible) dynamical systems, it is unclear why entropy is observed to approach a maximum. Setting aside the possibility that all of the laws of physics are incorrectly formulated, it is demonstrated that either observation of a subset of the complete dynamics (trivial coarse graining) or interactions with an external heat bath (addition of noise) may induce exactness with a consequent evolution of entropy to a maximal state.

Quantum gravity: an introduction to some recent results

Abstract: This article presents a general overview of the problems involved in the application of the quantum principle to a theory of gravitation. The ultraviolet divergences that appear in any perturbative computation are reviewed in some detail, and it is argued that it is unlikely that any theory based on local quantum fields could be consistent. This leads in a natural way to a supersymmetric theory of extended objects as the next candidate theory to study. An elementary introduction to superstrings closes the review, and some speculations about the most promising avenues of research are offered.

Pairing fluctuations in rapidly rotating nuclei

Abstract: Empirical evidence for the existence of pair fluctuations in rapidly rotating nuclei in connection with the pair gap is reviewed. The quantities considered are single-particle energies (routhians) and alignments. While the cranked shell model in the presence of static pair correlations provides an accurate description of data at rotational frequencies below the critical frequency corresponding to the collapse of the static pair gap, conspicuous discrepancies are found in the region of and above the pairing phase transition. In particular, a group of excitations is observed displaying lower excitation energies and smaller alignments than those predicted by the cranked shell model. Such excitations can be characterized as behaving as if the correlations induced by the presence of a pairing condensate were not totally obliterated after the "phase transition." A theoretical model, based on the renormalization of the single-particle motion mixed by the coupling to pairing vibrations, is quite successful in explaining the overall trend of the data at rotational frequencies larger than the critical frequency. Smaller alignments and excitation energies are correlated with configurations displaying particle coupling schemes which profit most from fluctuations of the pair gap about its zero equilibrium value. While this model reproduces many of the experimental features, it still overpredicts the alignments by 2-3 units of $\ensuremath{\hbar}$ in the crossing region. Thus other degrees of freedom (both static and dynamic), e.g., deformations, also must play a role at large rotational frequencies.

Cosmological helium production simplified

Abstract: The authors present a simplified model of helium synthesis in the early universe. The purpose of the model is to explain clearly the physical ideas relevant to the cosmological helium synthesis in a manner that does not overlay these ideas with complex computer calculations. The model closely follows the standard calculation, except that it neglects the small effect of Fermi-Dirac statistics for the leptons. The temperature difference between photons and neutrinos during the period in which neutrons and protons interconvert is also neglected. These approximations permit the expression of neutron-proton conversion rates in a closed form, which agrees to 10% accuracy or better with the exact rates. Using these analytic expressions for the rates, the authors reduce the calculation of the neutron-proton ratio as a function of temperature to a simple numerical integral. They also estimate the effect of neutron decay on the helium abundance. Their result for this quantity agrees well with precise computer calculations. Their semianalytic formulas are used to determine how the predicted helium abundance varies with such parameters as the neutron lifetime, the baryon-to-photon ratio, the number of neutrino species, and a possible electron-neutrino chemical potential.

Measurements of electron impact optical excitation functions

Abstract: Optical excitation function measurements for electron-atom and electron-ion collisions are reviewed. Sources of experimental error are discussed and, for cases in which adequate documentation is provided, publications are reviewed for accuracy of experimental method. The effects of polarization of the emitted radiation and methods of normalization are considered. The reliability of specific reported data is discussed based on these considerations, on the results of consistency checks, and, where possible, on comparison with other measurements. Data sources for 50 atoms and 20 atomic ions are identified. Comparative plots are presented for cases in which enough data are available: H, $\mathrm{He}(n^{1}S, n^{1}P, n^{1}D, 4^{3}S, 3^{3}P)$, ${\mathrm{He}}^{+}$, Ne, ${\mathrm{Ne}}^{+}$, Ar, ${\mathrm{Ar}}^{+}$, Xe, Li, Na, K, Mg, ${\mathrm{Mg}}^{+}$, Ca, Sr, ${\mathrm{Sr}}^{+}$, Cu, ${\mathrm{Zn}}^{+}$, Cd, Hg, and Mn.

Physics of digital devices

Abstract: Large computing machines have been built from relays, vacuum tubes, and transistors. Strenuous efforts to develop computing technology based on other devices have failed. The relay, vacuum tube, and transistor are three-terminal devices, and the essential physical factors that account for their success are described and used to discuss the reasons for the failure of other devices.

Observations in Particle Physics From Two Neutrinos to the Standard Model

Abstract: The lecture delivered on the presentation of the 1988 Nobel Prize in Physics is reprinted. The author describes the development of the standard Model of elementary particles through a series of experiments studying leptons. (AIP)

The first high-energy neutrino experiment

Abstract: The lecture delivered at the presentation of the 1988 Nobel Prize in Physics is reprinted. (AIP)

Experiments with high-energy neutrino beams

Abstract: The lecture delivered at the presentation of the 1988 Nobel Prize in Physics is reprinted The author describes some uses of neutrino beams of such as studying weak neutral currents, the Weinberg angle, and QCD (AIP)