Showing papers in "Reviews of Modern Physics in 1990"

Reaction-rate theory: fifty years after Kramers

Abstract: The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Coherent states: Theory and some Applications

Abstract: In this review, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented. The result is that, for a given dynamical group, the coherent states are isomorphic to a coset space of group geometrical space. Thus the topological and algebraic structure of the coherent states as well as the associated dynamical system can be extensively discussed. In addition, a quantum-mechanical phase-space representation is constructed via the coherent-state theory. Several useful methods for employing the coherent states to study the physical phenomena of quantum-dynamic systems, such as the path integral, variational principle, classical limit, and thermodynamic limit of quantum mechanics, are described.

Superconductivity in narrow-band systems with local nonretarded attractive interactions

Abstract: In narrow-band systems electrons can interact with each other via a short-range nonretarded attractive potential. The origin of such an effective local attraction can be polaronic or it can be due to a coupling between electrons and excitons or plasmons. It can also result from purely chemical (electronic) mechanisms, especially in compounds with elements favoring disproportionation of valent states. These mechanisms are discussed and an exhaustive list of materials in which such local electron pairing occurs is given. The authors review the thermodynamic and electromagnetic properties of such systems in several limiting scenarios: (i) Systems with on-site pairing which can be described by the extended negative-$U$ Hubbard model. The strong-attraction limit of this model, at which it reduces to a system of tightly bound electron pairs (bipolarons) on a lattice, is extensively discussed. These electron pairs behaving as hard-core charged bosons can exhibit a superconducting state analogous to that of superfluid $^{4}\mathrm{He}$ II. The change-over from weak-attraction BCS-like superconductivity to the superfluidity of charged hard-core bosons is examined. (ii) Systems with intersite pairing described by an extended Hubbard model with $Ug0$ and nearest-neighbor attraction and/or nearest-neighbor spin exchange as well as correlated hopping. (iii) A mixture of local pairs and itinerant electrons interacting via a charge-exchange mechanism giving rise to a mutually induced superconductivity in both subsystems. The authors discuss to what extent the picture of local pairing, and in particular superfluidity of hard-core charged bosons on a lattice, can be an explanation for the superconducting and normal-state properties of the high-${T}_{c}$ oxides: doped BaBi${\mathrm{O}}_{3}$ and the cuprates.

Properties of boson-exchange superconductors

Abstract: The author reviews some of the important successes achieved by Eliashberg theory in describing the observed superconducting properties of many conventional superconductors. Functional derivative techniques are found to help greatly in understanding the observed deviations from BCS laws. Approximate analytic formulas with simple correction factors for strong-coupling corrections embodied in the single parameter $\frac{{T}_{c}}{{\ensuremath{\omega}}_{\mathrm{ln}}}$ are also found to be very helpful. Here ${T}_{c}$ is the critical temperature and ${\ensuremath{\omega}}_{\mathrm{ln}}$ is an average boson energy mediating the pairing potential in Eliashberg theory. In view of the discovery of high-${T}_{c}$ superconductivity in the copper oxides, results in the very strong coupling limit of $\frac{{T}_{c}}{{\ensuremath{\omega}}_{\mathrm{ln}}}\ensuremath{\sim}1$ are also considered, as is the asymptotic limit when $\frac{{T}_{c}}{{\ensuremath{\omega}}_{\mathrm{ln}}}\ensuremath{\rightarrow}\ensuremath{\infty}$. This case is of theoretical interest only, but it is nevertheless important because simple analytic results apply that give insight into the more realistic strong-coupling regime. A discussion more specific to the oxides is included in which it is concluded that some high-energy boson-exchange mechanism must be operative, with, possibly, some important phonon contribution in some cases. A more definitive application of boson-exchange models to the oxides awaits better experimental results.

Supernova mechanisms. [SN 1987a]

Abstract: Supernovae of Type II occur at the end of the evolution of massive stars. The phenomenon begins when the iron core of the star exceeds a Chandrasekhar mass. The collapse of that core under gravity is well understood and takes a fraction of a second. To understand the phenomenon, a detailed knowledge of the equation of state at the relevant densities and temperatures is required. After collapse, the shock wave moves outward, but probably does not succeed in expelling the mass of the star. The most likely mechanism to do so is the absorption of neutrinos from the core by the material at medium distances. Observations and theory connected with SN 1987A are discussed, as are the conditions just before collapse and the emission of neutrinos by the collapsed core.

Boundary conditions for open quantum systems driven far from equilibrium

Abstract: This is a study of simple kinetic models of open systems, in the sense of systems that can exchange conserved particles with their environment. The system is assumed to be one dimensional and situated between two particle reservoirs. Such a system is readily driven far from equilibrium if the chemical potentials of the reservoirs differ appreciably. The openness of the system modifies the spatial boundary conditions on the single-particle Liouville---von Neumann equation, leading to a non-Hermitian Liouville operator. If the open-system boundary conditions are time reversible, exponentially growing (unphysical) solutions are introduced into the time dependence of the density matrix. This problem is avoided by applying time-irreversible boundary conditions to the Wigner distribution function. These boundary conditions model the external environment as ideal particle reservoirs with properties analogous to those of a blackbody. This time-irreversible model may be numerically evaluated in a discrete approximation and has been applied to the study of a resonant-tunneling semiconductor diode. The physical and mathematical properties of the irreversible kinetic model, in both its discrete and its continuum formulations, are examined in detail. The model demonstrates the distinction in kinetic theory between commutator superoperators, which may become non-Hermitian to describe irreversible behavior, and anticommutator superoperators, which remain Hermitian and are used to evaluate physical observables.

Dipole glass and ferroelectricity in random-site electric dipole systems

Abstract: This review covers recent experimental and theoretical investigations into cooperative phenomena in crystals containing off-center ions. These phenomena have attracted much attention in recent years because of a general interest in disordered systems, in particular in spin glasses, whose electrical analog is the dipole glass. Specific features of the dipole glass state in alkali halide crystals with off-center ions are discussed and compared with spin glasses. Experimental studies performed in recent years have demonstrated that off-center ions in highly polarizable crystals can at certain concentrations induce ferroelectric domains with regions of macroscopic spontaneous polarization. The physical causes of this phenomenon are examined and some physical properties of crystals exhibiting such an impurity-induced phase transition are analyzed. Primary emphasis is placed on the range of low impurity concentrations, where system properties differ substantially from predictions of mean-field theory.

Theory of semiconductor superlattice electronic structure

Abstract: The authors review the theory of semiconductor superlattice electronic structure. First a survey of theoretical methods is presented. These methods can be divided into two general classes: the supercell approach in which the superlattice is viewed as a material with a large unit cell, and the boundary-condition approach in which bulk wave functions in the constituent semiconductors are matched at the superlattice interfaces. Supercell approaches are essentially the same as conventional band-structure methods. They can only be applied to thin-layer superlattices because of numerical cost. The authors discuss problems of interface matching that occur in various boundary-condition methods and relate these methods to each other. A particular boundary-condition method is used to discuss the electronic structure of various III-V semiconductor superlattices. Emphasis is placed on discussing the qualitatively different behavior that can arise because of different energy-band lineups, strain conditions, and growth orientations. The authors compare the results of three commonly used boundary-condition methods and find generally good agreement.

Molecular vibrational and rotational motion in static and dynamic electric fields

Abstract: For many years the effects of a static or dynamic electric field upon electronic motion in a molecule have been studied. These effects have been described in terms of multipolar electronic polarizabilities and higher-order hyperpolarizabilities. Much less attention, however, has been paid to the effects of an electric field upon vibrational and rotational motion. It is the aim of this review to consider, in some detail, these effects. As in the electronic work, they too will be described in terms of polarizabilities and hyperpolarizabilities (the latter being particularly important for the study of nonlinear optics). The theory will be developed so as to bring together the different methods that have been used in various calculations. Examples drawn from the recent literature will be discussed and it will be seen that in many cases vibrational and rotational changes with an electric field are as important as electronic ones, if not more so. Examples of experimental work relevant to this review include research on the Kerr effect, electric-field-induced second-harmonic generation, and third-harmonic generation.

Intensity interferometry in subatomic physics

Abstract: The intensity interferometry technique, commonly referred to as the Hanbury-Brown/Twiss effect, has been applied to nuclear and elementary-particle collisions as a method of investigating their space-time evolution. In this review the theoretical framework of the technique is presented, describing the formulations in common use. A survey is made of its application to subatomic collisions, ranging from high-energy elementary-particle reactions to low-energy nuclear reactions. Results derived from experimental data analysis are compiled and discussed. A critique is made of the interpretational difficulties associated with the use of the technique in reaction studies.

Experiments with an isolated subatomic particle at rest

Abstract: The author discusses both philosophy and experimental evidence regarding subatomic particles at rest. The size and weight of subatomic particles are discussed. The author's views on composite electron and quartz models are presented. >

Intrinsic states of deformed odd-A nuclei in the mass regions (151 221)

Abstract: A review of the empirical data on intrinsic states of odd-$A$ nuclei in the mass range $151\ensuremath{\le}A\ensuremath{\le}193$ and $A\ensuremath{\ge}221$ is presented. Global summaries of the data are presented in tables for each isotopic and isotonic chain, wherein the excitation energy, the $log\mathrm{ft}$ values, the moment-of-inertia parameter, and the decoupling parameter (for $K=\frac{1}{2}$ bands) are listed for single-particle, vibrational admixed, and pure vibrational states. Similar data are separately presented for three-quasiparticle excitations in the rare-earth region. Taking guidance from the systematics on nuclear deformation, the single-particle deformed potential for axially symmetric and reflection-symmetric shapes (the Nilsson model) modified by the hexadecapole deformation is used to interpret the data. Other variations of the Nilsson model, which include axially asymmetric shapes ($\ensuremath{\gamma}$ deformation) and especially reflection-asymmetric shapes (octupole deformation), have also been used to interpret the data in certain limited regions. Systematics for the intrinsic excitations are presented and discussed in terms of these models. The newly emerging regions of the octupole-quadrupole deformation and superdeformation are also discussed.

Theory of the soft-x-ray edge problem in simple metals: historical survey and recent developments

Abstract: In the first half of this article, theoretical treatments of the infrared divergence involved in the edge problem of soft-x-ray absorption, emission, and photoemission spectra of simple metals are reviewed historically. In the second half, recent developments in the work of the present authors using the Fermi golden rule are described to show that the method permits an analytical treatment and provides exact results for various aspects of the edge problem.

The temperature-dependent electrical resistivities of the alkali metals

Abstract: This review contains a comprehensive examination of all modern measurements and calculations of the temperature-dependent electrical resistivity $\ensuremath{\rho}(T)$ for the alkali metals---and especially potassium (K)---from their melting points down to below 0.1 K. The simplicity of the electronic structures of these metals makes them unique for testing our fundamental understanding of $\ensuremath{\rho}(T)$. At all temperatures down to a few K, $\ensuremath{\rho}(T)$ is dominated by its electron-phonon scattering component, ${\ensuremath{\rho}}_{\mathrm{ep}}(T)$. Current quantitative understanding of ${\ensuremath{\rho}}_{\mathrm{ep}}(T)$ in the alkali metals is examined in detail, including effects of phonon drag at temperatures below \ensuremath{\simeq} 10 K. In the vicinity of 1 K, $\ensuremath{\rho}(T)$ in pure, unperturbed, bulk alkali metals is predicted to be dominated by electron-electron scattering. ${\ensuremath{\rho}}_{\mathrm{ee}}(T)={A}_{\mathrm{ee}}{T}^{2}$. In disagreement with previous reviews, the authors argue that ${A}_{\mathrm{ee}}$ is nearly constant for each alkali metal and---at least for K---also in quantitative agreement with calculation. Below 1 K, alloys based on K and lithium display both previously predicted and completely unexpected effects. Perturbations such as deformation and thinning of K wires induce unusual and interesting behaviors. An unexpected Kondo-like effect appears when K contacts polyethylene. Charge-density-wave-based predictions of contributions to $\ensuremath{\rho}(T)$ in the alkali metals are also considered. Three appendices examine (a) what is involved in a realistic calculation of $\ensuremath{\rho}(T)$; (b) the experimental problems encountered in high-precision measurements of $\ensuremath{\rho}(T)$ at low temperatures and how they are solved; and (c) the most recent experimental data concerning charge-density waves in the alkali metals.

Theories of the origin of the solar system 1956- 1985

Abstract: Attempts to find a plausible naturalistic explanation of the origin of the solar system began about 350 years ago but have not yet been quantitatively successful. The period 1956- 1985 includes the first phase of intensive space research; new results from lunar and planetary exploration might be expected to have played a major role in the development of ideas about lunar and planetary formation. While this is indeed the case for theories of the origin of the moon (selenogony), it was not true for the solar system in general, where ground-based observations (including meteorite studies) were frequently more decisive. During this period most theorists accepted a monistic scenario: the collapse of a gas-dust cloud to form the sun with surrounding disk, and condensation of that disk to form planets, were seen as part of a single process. Theorists differed on how to explain the distribution of angular momentum between sun and planets, on whether planets formed directly by condensation of gaseous protoplanets or by accretion of solid planetesimals, on whether the "solar nebula" was ever hot and turbulent enough to vaporize and completely mix its components, and on whether an external cause such as a supernova explosion "triggered" the initial collapse of the cloud. Only in selenogony was a tentative consensus reached on a single working hypothesis with quantitative results.

The number of neutrino species

Abstract: The authors review the methods used before the operation of the high energy Stanford and CERN ${e}^{+}{e}^{\ensuremath{-}}$ colliders to determine the number of neutrino species ${N}_{\ensuremath{ u}}$, or an upper limit on this number, within the framework of the Standard Model of light stable neutrinos interacting according to the SU(2)\ifmmode\times\else\texttimes\fi{}U(1) universal couplings. The astrophysical limit based on the neutrino burst from supernova 1987A is discussed first, followed by a discussion of the cosmological constraint based on the observed He/H abundance ratio. Finally, the particle physics methods based on single-photon production in ${e}^{+}{e}^{\ensuremath{-}}$ collisions, on the production of monojets in $p\overline{p}$ collisions, and on the determination of ${N}_{\ensuremath{ u}}$ from the ratio of the $W\ensuremath{\rightarrow}l\overline{\ensuremath{ u}}$ to ${Z}^{0}\ensuremath{\rightarrow}l\overline{l}$ partial cross sections in $p\overline{p}$ collisions are discussed. The various sources of uncertainty and the experimental backgrounds are presented, as well as an idea of what may be expected on this subject in the future. There is a remarkable agreement between the various methods, with central values for ${N}_{\ensuremath{ u}}$ between 2 and 3 and with upper limits ${N}_{\ensuremath{ u}}l6$. Combining all determinations, the authors obtain a central value ${N}_{\ensuremath{ u}}={2.1}_{\ensuremath{-}0.4}^{+0.6}$ for ${m}_{\mathrm{top}}=50$ GeV/${\mathit{c}}^{2}$ and ${N}_{\ensuremath{ u}}={2.0}_{\ensuremath{-}0.4}^{+0.6}$ if ${m}_{\mathrm{top}}\ensuremath{\ge}{m}_{W}$. The results are perfectly compatible with the a priori knowledge that at least three families of neutrinos should exist. The observed consistency between this a priori knowledge, the laboratory determinations of ${N}_{\ensuremath{ u}}$, and determinations from SN 1987A and cosmology represent an astounding success for the Standard Model and for the current descriptions of stellar collapse and the Big-Bang primordial nucleosynthesis. These results, however, severely limit the number of additional families. Although the consistency is significantly worse, four families still provide a reasonable fit. In the framework of the Standard Model, a fifth light neutrino is, however, unlikely. A noted added in proof summarizes the results recently obtained at the Fermilab $\overline{p}p$ and the Stanford and CERN ${e}^{+}{e}^{\ensuremath{-}}$ colliders which confirm these conclusions.