This article describes recent technical developments that have made the total-energy pseudopotential the most powerful {ital ab} {ital initio} quantum-mechanical modeling method presently available. In addition to presenting technical details of the pseudopotential method, the article aims to heighten awareness of the capabilities of the method in order to stimulate its application to as wide a range of problems in as many scientific disciplines as possible.

This article describes recent technical developments that have made the total-energy pseudopotential the most powerful ab initio quantum-mechanical modeling method presently available. In addition to presenting technical details of the pseudopotential method, the article aims to heighten awareness of the capabilities of the method in order to stimulate its application to as wide a range of problems in as many scientific disciplines as possible.

The Nambu-Jona-Lasinio model is reviewed in its flavor SU(2) and SU(3) versions applied to quarks. The dynamical generation of quark masses is demonstrated as a feature of chiral symmetry breaking. One finds that the associated meson spectra, as well as the meson static properties, can be well described. Current-algebra results, which arise as a consequence of symmetry considerations, automatically hold for this model and are explicitly demonstrated to do so. These include the Goldberger-Treiman and Gell-Mann-Oakes-Renner relations. Effects of finite temperature, finite chemical potential, and strong Maxwell and chromoelectromagnetic fields on the dynamically generated quark mass and the meson spectra are discussed. The alternative procedure of bosonization to obtain an effective Lagrange density in mesonic degrees of freedom, using the derivative expansion, is also presented. The current status in relating the results of this model to that of chiral perturbation theory is critically examined.

A review of classical percolation theory is presented, with an emphasis on novel applications to statistical topography, turbulent diffusion, and heterogeneous media. Statistical topography involves the geometrical properties of the isosets (contour lines or surfaces) of a random potential psi(x). For rapidly decaying correlations of psi, the isopotentials fall into the same universality class as the perimeters of percolation clusters. The topography of long-range correlated potentials involves many length scales and is associated either with the correlated percolation problem or with Mandelbrot's fractional Brownian reliefs. In all cases, the concept of fractal dimension is particularly fruitful in characterizing the geometry of random fields. The physical applications of statistical topography include diffusion in random velocity fields, heat and particle transport in turbulent plasmas, quantum Hall effect, magnetoresistance in inhomogeneous conductors with the classical Hall effect, and many others where random isopotentials are relevant. A geometrical approach to studying transport in random media, which captures essential qualitative features of the described phenomena, is advocated.

The discovery of periodic conductance oscillations as a function of charge density in very small transistors has led to a new understanding of the behavior of electrons in such small structures. It has been demonstrated that, whereas a conventional transistor turns on only once as electrons are added to it, submicronsize transistors, isolated from their leads by tunnel junctions, turn on and off again every time an electron is added. This unusual behavior is primarily the result of the quantization of charge and the Coulomb interaction between electrons on the small transistor. However, recent experiments demonstrate that the quantization of energy is important as well.

We first show that, with the same input parameters, the standard solar models of Bahcall and Ulrich; of Sienkiewicz, Bahcall, and Paczynski; of Turck-Chieze, Cahen, Casse, and Doom; and of the current Yale code all predict event rates for the chlorine experiment that are the same within +/-0.1 SNU (solar neutrino units), i.e., approximately 1% of the total calculated rate. We then construct new standard solar models using the Yale stellar evolution computer code supplemented with a more accurate (exportable) nuclear energy generation routine, an improved equation of state, recent determinations of element abundances, and the new Livermore (OPAL) opacity calculations. We evaluate the individual effects of different improvements by calculating a series of precise models, changing only one aspect of the solar model at a time. We next add a new subroutine that calculates the diffusion of helium with respect to hydrogen with the aid of the Bahcall-Loeb formalism. Finally, we compare the neutrino fluxes computed from our best solar models constructed with and without helium diffusion. We find that helium diffusion increases the predicted event rates by about 0.8 SNU, or 11% of the total rate, in the chlorine experiment; by about 3.5 SNU, or 3%, in the gallium experiments; and by about 12% in the Kamiokande and SNO experiments. The best standard solar model including helium diffusion and the most accurate nuclear parameters, element abundances, radiative opacity, and equation of state predicts a value of 8.0+/-3.0 SNU for the Cl-37 experiment and 132(-17)+21 SNU for the Ga-71 experiment. The quoted errors represent the total theoretical range and include the effects on the model predictions of 3sigma errors in measured input parameters. All 15 calculations since 1968 of the predicted rate in the chlorine experiment given in this series of papers are consistent with both the range estimated in the present work and the 1968 best-estimate value of 7.5+/-2.3 SNU. Including the effects of helium diffusion and the other improvements in the description of the solar interior that are implemented in this paper, the inferred primordial solar helium abundance is Y=0.273. The calculated depth of the convective zone is R = 0.707R., in agreement with the value of 0.713R. inferred by Christensen-Dalsgaard, Gough, and Thompson from a recent analysis of the observed p-mode oscillation frequencies. Including helium diffusion increases the calculated present-day hydrogen surface abundance by about 4%, decreases the helium abundance by approximately 11%, and increases the calculated heavy-element abundance by about 4%. In the Appendix, we present detailed numerical tables of our best standard solar models computed both with and without including helium diffusion. In the context of the MSW (Mikheyev-Smirnov-Wolfenstein) or other weak-interaction solutions of the solar neutrino problem, the numerical models can be used to compute the influence of the matter in the sun on the observed neutrino fluxes.

Symplectic maps are the discrete-time analog of Hamiltonian motion. They arise in many applications including accelerator, chemical, condensed-matter, plasma, and fluid physics. Twist maps correspond to Hamiltonians for which the velocity is a monotonic function of the canonical momentum. Twist maps have a Lagrangian variational formulation. One-parameter families of twist maps typically exhibit the full range of possible dynamics-from simple or integrable motion to complex or chaotic motion. One class of orbits, the minimizing orbits, can be found throughout this transition; the properties of the minimizing orbits are discussed in detail. Among these orbits are the periodic and quasiperiodic orbits, which form a scaffold in the phase space and constrain the motion of the remaining orbits. The theory of transport deals with the motion of ensembles of trajectories. The variational principle provides an efficient technique for computing the flux escaping from regions bounded by partial barriers formed from minimizing orbits. Unsolved problems in the theory of transport include the explanation for algebraic tails in correlation functions, and its extension to maps of more than two dimensions.

Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counter examples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.

A review is given of our present knowledge of collective spin-isospin excitations in nuclei. Most of this knowledge comes from intermediate-energy charge-exchange reactions and from inelastic electron- and proton-scattering experiments. The nuclear-spin dynamics is governed by the spin-isospin-dependent two-nucleon interaction in the medium. This interaction gives rise to collective spin modes such as the giant Gamow-Teller resonances. An interesting phenomenon is that the measured total Gamow-Teller transition strength in the resonance region is much less than a model-independent sum rule predicts. Two physically different mechanisms have been discussed to explain this so-called quenching of the total Gamow-Teller strength: coupling to subnuclear degrees of freedom in the form of DELTA-isobar excitation and ordinary nuclear configuration mixing. Both detailed nuclear structure calculations and extensive analyses of the scattering data suggest that the nuclear configuration mixing effect is the more important quenching mechanism, although subnuclear degrees of freedom cannot be ruled out. The quenching phenomenon occurs for nuclear-spin excitations at low excitation energies (omega approximately 10-20 MeV) and small-momentum transfers (q less-than-or-equal-to 0.5 fm-1). A completely opposite effect is anticipated in the high (omega,q)-transfer region (0 less-than-or-equal-to omega less-than-or-equal-to 500 MeV, 0.5 less-than-or-equal-to 0.5 less-than-or-equal-to q less-than-or-equal-to 3 fm-1). The nuclear spin-isospin response might be enhanced due to the attractive pion field inside the nucleus. Charge-exchange reactions at GeV incident energies have been used to study the quasifree peak region and the DELTA-resonance region. An interesting result of these experiments is that the DELTA-excitation in the nucleus is shifted downwards in energy relative to the DELTA-excitation of the free proton, The physical origin of this shift is discussed, and it is shown that it may be related to the energy-dependent, attractive one-pion exchange interaction in the medium.

Hydrogen interactions with imperfections in crystalline metals and semiconductors are reviewed. Emphasis is given to mechanistic experiments and theoretical advances contributing to predictive understanding. Important directions for future research are discussed.

The fundamental theory of the geometric phase is summarized in a way suitable for use in molecular systems treated by the Born-Oppenheimer approach. Both Abelian and non-Abelian cases are considered. Applications discussd include the Abelian geometric phase associated with an intersection of two electronic potential-energy surfaces; screening of nuclei by the electrons from an external magnetic field; non-Abelian gauge potentials in molecular systems with Kramers degeneracy; and the coupling between different electronic levels (Born-Oppenheimer breakdown) represented as a gauge potential. Experimental tests for these systems are discussed, as well as a number of experiments on spin systems.

This article reviews the discovery, exploration, and application of negative-ion resonances in inelastic electron scattering by molecules adsorbed on surfaces. A major theme of the review is the degree to which the properties of resonances in free molecules are perturbed by adsorption. The influence of the surface upon the energy, lifetime (width), symmetry, and decay channels of molecular resonances is discussed, in the light of both experimental and theoretical studies of a wide range (from diatomic molecules to polymers) of both weakly bound (physisorbed) and strongly bound (chemisorbed) molecules. The metallic image potential, electron scattering by the atoms of the surface, and chemical bonding in chemisorption systems are found to be key factors in determining the energy, width, and symmetry of resonances in molecular adsorbates. In the case of oriented adsorbed molecules, the angular distribution of scattered electrons is found to reflect not only the symmetry of the resonant state (as in the gas phase), but also the orientation of the molecular axis. Coherent elastic electron scattering by the surface can modulate the angular distributions, as well as the shape of the resonance profile. Selection rules that govern the observed resonance behavior are discussed. A further consequence of adsorption is the enrichment of the range of channels into which resonances may decay, and the excitation of both molecule-surface and intermolecular vibrational modes has been established. The article concludes with an evaluation of future prospects for the investigation and application of resonances in adsorbed molecules.

All known data on the energy distribution of secondary electrons from collisions of protons with atoms and molecules have been reviewed and differential cross sections have been collected. The two experimental methods used to obtain the data are discussed and possible sources of error pointed out. Theoretical treatments are reviewed and several methods of checking the consistency of the data are discussed. Two semiempirical models have been chosen to represent the differential cross sections, and parameters for these models are given which fit the average of the experimental data, subject to known constraints. Recommended values of differential cross sections are given for ten target gases by means of these models.

On the basis of current physical understanding, it is impossible to predict with confidence the interior constitution of neutron stars. Cooling of neutron stars provides a possible way of discriminating among possible states of matter within them. In the standard picture of cooling by neutrino emission developed over the past quarter of a century, neutron stars are expected to cool relatively slowly if their cores are made up of nucleons, and to cool faster if matter is in an exotic state, such as a pion condensate, a kaon condensate, or quark matter. This view has recently been called into question by the discovery of a number of other processes that could lead to copious neutrino emission and rapid cooling.

Bak, Tang, and Wiesenfeld proposed the idea of self-organized criticality in order to gain a general understanding of the behavior of extended dynamical systems driven in a nonequilibrium state. In particular this idea was intended to explain the ubiquitous scaling behavior and fractal structures that are observed in many different phenomena occurring spontaneously in nature. Recent experiments on the dynamics of a pile of sand, which had been expected to show self-organized criticality, are reviewed and it is shown that sand behaves in a manner more reminiscent of a first-order transition than of a second order (or critical) one.

This paper reviews the progress made in the last few years in theoretical understanding of the properties of superconductors in very high magnetic fields. The key ingredient in the new understanding is the recognition that the usual negative effect of orbital frustration in a superconducting state, reflected in diamagnetic pair breaking, is obviated when all electrons reside in only the few lowest Landau levels. A new relation between the superconducting order parameter and the magnetic field now exists which permits a strong enhancement of the critical temperature with increasing magnetic field. The issue of Pauli pair breaking and the effect of impurities in this new state are also discussed, along with the important observation that the attractive component of the effective electron-electron interaction in systems with low carrier density is enhanced with increasing magnetic field. While this paper emphasizes the theoretical aspects of this high-field limit, it does present a unified picture of superconductivity throughout the whole temperature and magnetic-field phase diagram. Numerical applications to simple models of low-carrier-density semiconductors and semimetals are also discussed, since these materials are the most likely candidates for this new phase.

This paper provides a theoretical framework for the high-precision (less-than-or-greater-than 1%) electroweak experiments that are likely to be done in the next ten years. The authors have collected the Standard Model (SM) predictions of 14 weak neutral-current observables and 15 W and Z properties to the one-loop level and have calculated the deviations that would be caused by ten general types of possible new physics that enter at the tree or loop level. Certain experiments appear to have special promise as probes of the new physics considered here. Most importantly, a systematic procedure is introduced that provides a prescription for the analysis of future experimental data and the means of delineating the nature of new physics if quantitative deviations from SM predictions are observed.

Planar systems admit quantum states that are neither bosons nor fermions, i.e., whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar models in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles. The appropriate generalization of statistics is also discussed. Some physical effects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Field-theoretical models in 2 + 1 dimensions are presented which admit solitons that carry fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Fock states carry fractional spin and statistics are discussed.

The random distribution of impurities in a semiconductor host lattice introduces potential fluctuations that allow energy levels within the forbidden energy gap. This statistical effect distorts the unperturbed density of states of the pure semiconductor, and, at high doping concentrations, substantial band tails appear. The changes in the density-of-states function are particularly important in determining the number of free carriers in a heavily doped semiconductor. Together with many-particle interactions, band tailing constitutes one of the most significant heavy-doping effects. Although the band-tailing phenomenon bas been studied for many years, only a one-dimensional analytical model, which assumes a Gaussian white-noise probability distribution of the potential fluctuation, exists. In this paper the different classes of theories that describe this band tailing of the density of states in heavily doped semiconductors are reviewed in detail.