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.
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 T(c)/omega-ln are also found to be very helpful. Here T(c) is the critical temperature and omega-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 T(c)/omega-ln approximately l are also considered, as is the asymptotic limit when T(c)/omega-ln > infinity. 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.
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.
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.
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.