Showing papers in "Physics Reports in 1986"

Abstract: Abundances of strange antibaryons formed in nuclear collisions at above 10 GeV/A are considered as a most accessible diagnostic tool for the study of the possible formation and physical properties of the quark-gluon plasma phase of hadronic matter. In this report we describe the current status and develop a dynamical approach in order to describe strange particle formation in nuclear collisions at high energy.

Abstract: We review the recent progress in extracting the equation of state of hot dense hadronic matter from relativistic heavy ion collisions. At first a discussion of the bulk properties of infinite nuclear matter is presented. Next the theoretical approaches are developed which describe the complicated dynamics and non-equilibrium features in actual high energy nucleus-nucleus collisions: Nuclear fluid dynamics, the intranuclear cascade model, classical equation of motion simulations, the Vlasov Uehling-Uhlenbeck theory and the time dependent Dirac equation with meson field dynamics are exhibited. The recent experimental confirmation of the early hydrodynamic predictions on nuclear shock compression establishes the key mechanism for creating high nuclear density and temperatures in the laboratory, and thus the key mechanism for investigating the nuclear equation of state. Evidence for a suprisingly stiff nuclear equation of state is presented from a comparison of the distinct theoretical predictions to recent high multiplicity selected 4π data on fragment formation, pion production and collective sidewards flow. We also discuss the possible creation of a deconfined quark gluon plasma at future ultra-relativistic heavy ion facilities.

Abstract: This report gives an introduction to the Casimir effect in quantum field theory and its applications. The interaction between the vacuum of a quantized field and an external boundary or a classical external field is investigated laying particular emphasis on Casimir's concept of measurable change in the vacuum energy. The various methods for evaluation and regularization of the Casimir energy are discussed in detail for specific field configurations. Recent applications of the Casimir effect in supercritical fields, QCD bag models and electromagnetic media are reviewed.

Abstract: The theory of the semiclassical evolution of wave packets is developed as a version of WKB theory in phase space. Special attention is given to the transformation properties of wave packets, their Wigner functions, and their classical analogs under operations in phase space. A complete development of the Heisenberg and metaplectic operators is presented, including their interaction with the Wigner-Weyl formalism and the question of caustics. A metaplectically covariant wave packet propagator is presented and discussed. Finally, a group theoretical discussion of Gaussian wave packets is given.

Abstract: We review the recent developments on the Skyrme model in the context of QCD, and analyze their relevance to low-energy phenomenology. The fundamentals of chiral symmetry and PCAC are presented, and their importance in effective chiral models of the Skyrme type discussed. The nature and properties of skyrmions are thoroughly investigated, with particular stress on the basic role of the Wess-Zumino term. The conventional Skyrme model is extended to the low-lying vector meson resonances, and the rudiments of vector meson dominance are elucidated. A detailed account of the static and dynamical properties of nucleons and δ-isobars is presented. The relevance of the Skyrme model to the nuclear many-body problem is outlined and its importance for boson exchange models stressed.

Abstract: The gauge theory for strong interactions, QCD, has an apparent U(1) symmetry that is not realized in the real world. The violation of the U(1) symmetry can be attributed to a well-known anomaly in the regularization of the theory, which in field configurations called “instantons” can be seen to give rise to interactions that explicitly break the symmetry. A simple polynomial effective Lagrangian describes these effects qualitatively very well. In particular it is seen that no unwanted Goldstone bosons appear and the eta particle owes a large fraction of its mass to instantons. There is no need for field configurations with fractional winding numbers and it is explained how a spurious U(1) symmetry that remains in QCD even after introducing instantons, does not affect these results.

Abstract: String theories suggest particular forms for gravity interactions in higher dimensions We consider an interesting class of gravity theories in more than four dimensions, clarify their geometric meaning and discuss their special properties

Abstract: The purpose of this article is to present a review of the nonlinear effects associated with relativistic electron-mass variation and the ponderomotive force in unmagnetized as well as magnetized plasmas. Many high-frequency waves can become unstable with respect to the electron-mass modulation and the excitation of low-frequency density fluctuations. The nonlinear equations which govern the evolution of the modulationally unstable waves are derived. The phenomena of soliton formation, radiation collapse, and profile modification are investigated. Finite amplitude theories of the envelope solitons are reviewed. In a multidimensional situation, the electromagnetic waves can undergo self-focusing. The use of the variational methods allows one to calculate the nonlinear wavenumber and radius of the self-focused laser beams. Analytical solutions for the self-trapped radiation and the three-dimensional relativistic solitons are obtained. It is found that magnetized plasmas can support the propagation of new types of ultrarelativistic electromagnetic waves. The modulational instability of the latter is analyzed. Furthermore, it is shown that the relativistic ponderomotive force in a magnetized plasma can produce large amplitude field-aligned electrostatic potentials which can effectively accelerate particles to very high energies. Finally, we consider the nonlinear propagation of intense electromagnetic waves in electron-positron plasmas. Possible applications in inertial fusion, beat-wave particle accelerator, rf heating of magnetically confined plasmas, and pulsar radiation are pointed out.

Abstract: The stability of solitons is reviewed for nonlinear conservative media. The main attention is paid to the description of the methods: perturbation theory, inverse scattering transform, Lyapunov method. Its applications are demonstrated in detail for the nonlinear Schrodinger equation, the KdV equation, and their generalizations. Applications to problems in plasma physics and hydrodynamics are considered.

Abstract: The paper reviews the state-of-the-art in the observation and analytical description of localized electrostatic phase space structures. These structures occur on the Debye length scale and introduce a kind of intermittency in the dynamics of externally driven collisionless plasmas. Holes, the one group of structures investigated, are nonlinear saturated states of two-stream instabilities in which saturation is provided by particle trapping. They are ring-shaped vortices in phase space and are macroscopically manifest in local density depressions. Double layers, on the other hand, are narrow monotonic potential transitions and connect differently biased plasmas, resembling in some sense phase transitions. The controlling function of these nonlinearly excited d.c. states in the dynamical evolution of bounded plasmas exhibiting transient phenomena is discussed.

Abstract: The classical free motion of a mass point on a compact surface of constant negative curvature is the most chaotic possible. The quantal description of this motion is under development. In this review we (a) bring together the mathematical tools needed for the problem; (b) survey the classical results; (c) develop the quantal description; (d) discuss the relations between the classical and quantal results; (e) offer some conjectures towards the diagnosis of chaoticity in quantum systems. The text is divided into chapters and sections; each section ends with a brief summary which also serves as a local abstract. Chapter I gives the motivations. Chapter II describes various models of the pseudosphere, or Bolyai-Lobachevsky plane. Chapters III and IV analyse the classical motions constrained to surfaces of constant negative curvature, and the salient results on ergodicity, mixing, etc.… Chapters V and VI specify the quantum problem and exhibit the relevant mathematical tools. Chapter VII exhibits the remarkable exact connections between the classical and quantal results which are embodied in Selberg's trace formula or are consequences of it. Chapter VIII deals with the semiclassical connections between the two descriptions, including the quantal equivalents of such classical notions as the Liapunov exponent and the Poincare section map. Chapter IX contains some numerical results obtained by C. Schmit on the spectrum of a simple case, in particular on its fluctuations and their interpretation. Chapter X summaries our conclusions. The Appendices from A to N are integral parts of the review and are only separated from the text in order not to interrupt the flow. They contain details which clarify mathematical or conceptual points. Similarly, the figures should also be used to complement and clarify the text.

Abstract: This paper examines single-mode and two-mode Gaussian pure states (GPS), quantum mechanical pure states with Gaussian wave functions. These states are produced when harmonic oscillators in their ground states are exposed to potentials, or interaction Hamiltonians, that are linear or quadratic in the position and momentum variables (i.e., annihilation and creation operators) of the oscillators. The physical and group theoretical properties of these Hamiltonians and the unitary operators they generate are discussed. These properties lead to a natural classification scheme for GPS. Important properties of single-mode and two-mode GPS are discussed. An efficient vector notation is introduced, and used to derive many of the important properties of GPS and of the Hamiltonians and unitary operators associated with them.

Abstract: Various techniques for the computation of the fractional fermion number of topological solitons are reviewed. First the original calculation by Jackiw and Rebbi and the relevance of fermion number fractionization in polymer physics are discussed. Subsequently, techniques for computing the fermion number in increasingly more general models are developed with applications to one-dimensional solitons, vortices in 2 + 1 dimensions and 3 + 1 dimensional magnetic monopoles. At each stage the connections between the fermion number calculation and the general properties of the spectrum, in particular the spectral asymmetry of the pertinent Dirac operator are exposed. Topological methods for computing the fermion number are developed for a large class of Dirac Hamiltonians. The adiabatic method of Goldstone and Wilczek is then introduced and applied to the Skyrme model. Finally, an exact technique for the computation of the fermion number is developed by deriving an open space generalization of the Atiyah-Patodi-Singer index theorem and as an application the baryon number of a chiral bag is computed.

Abstract: The recent subject of weak localization is an important area of research in condensed matter physics which has received a considerable amount of experimental and theoretical attention. In its existing form, the theory is founded entirely on the impurity technique of Green's function. In this paper, we present a theory of weak localization which is put rigorously on a quasiclassical basis thus providing a more intuitive understanding. For example, it becomes apparent that much of the underlying physics is a result of quantum mechanical interference effects in a very elementary sense. It is one of those unique cases where the superposition principle of quantum mechanics leads to observable consequences in the properties of macroscopic systems. In addition, all the important quantitative results obtained so far are recovered in the present quasiclassical approach.

Abstract: A review is given of the wide variety of predictions that results from a Landau-type of description of the nematic-isotropic phase transition. This includes a discussion of the nature of the order parameter and of the various types of possible phases, of the influence of external fields, and of the effect of inclusion of spatial variations of the order parameter. The various predictions are compared with the available experimental results. It is concluded that there is still no clear picture about the nature of the singularity near the nematic-isotropic phase transition. Though the assumption of classical (mean-field) critical behaviour seems to be incorrect, there is no conclusive proof which alternative applies.

Abstract: When nuclei collide at beam energies from several tens of MeV to several GeV per nucleon considerable disorder is generated. Nuclear fragments ranging from nucleons all the way up in mass to the target and projectile nuclei themselves have been observed experimentally. Theoretical models for the dynamics of the formation and emission of these clusters of nucleons are reviewed. Most of the models, but not all, are statistical in origin, following from the assumption that the phase space available for cluster formation and emission is the dominant factor. The entropy generated during the collision may be studied in diverse dynamical models, such as intranuclear cascade and nuclear fluid dynamics. The entropy of the system may be estimated from the measured abundances of nuclear clusters, thus providing information on the properties of hot and dense nuclear matter. Critical analysis of both conventional and exotic interpretations of the data are given.

Abstract: Random percolation, self-avoiding walks or lattice animals can be regarded as static geometrical models where the different possible configurations are completely independent from each other and show no memory effects. These static geometrical models have extensively ben studied in the past. Certain configurations (clusters) were, for technical reasons, sometimes constructed by a growth process where computer time might be interpreted as a measure of time but then one had to make sure that the final result of the growth had the same statistical weight as the configuration of the static model. In nature, however, geometrical clusters (tumors, gels, soot) are usually grown. Thus we review studies of geometrical growth models as such in order to describe some real processes and to compare them with the static models. The growth of a single cluster as well as the growth of a distribution of clusters is of interest. Growth models can be studied as a function of dimensionality and of the specific rules of the growth. One can introduce anisotropy and mobility and even find universality classes in the sense of the theory of phase transitions. Up to now most work has been done with computer simulations but in some cases mean-field type approaches, e-expansions and transfer matrix calculations on strips are possible. We give a general overview on the subject. The paper begins with an introduction to the field of growth models showing what makes them different from stalic models. Much emphasis is then put on scaling relations and their numerical verification. A principal role in these relations plays the fractal dimension. Then a few models are briefly reviewed and only for some examples we will go into details. These examples are mainly kinetic gelation which is a kinetic generalization of percolation, epidemics which are growth models that produce percolation clusters and aggregation as an example for a model that has no static reference model.

Abstract: Recent data on the production of pions and strange particles at the Bevalac and Synchrophasotron accelerators are reviewed, covering pion spectra and multiplicity distributions, λ, K+ and K− yields and spectra, and Λ polarization. Emphasis is placed on recent progress in determining the equation of state of compressed fireball nuclear matter from the observed pion yield in central collisions. Further, the information derived from apparent spectral temperatures is critically examined, along with a discussion of thermal and chemical equilibrium attainment in the reactions, as revealed by particle spectra and yields.

Abstract: Analytical and numerical work on confinement phase transitions in finite-temperature Abelian and non-Abelian gauge theories is reviewed. These transitions are order-disorder transitions and their critical properties (if any) can be understood from the standard theory of critical phenomena. Strong coupling, large- N , and non-perturbative lattice methods are discussed. The role of matter fields as symmetry-breaking perturbations is noted as important to the eventual unraveling of the phase structure of quantum chromodynamics.

Abstract: The method of quasienergy states (QES) for describing a quantum system in the field of a monochromatic light wave is presented. The perturbation theory for QES and quasistationary (decay) QES is developed. Various methods of obtaining approximate Green functions of valence electrons in atoms used for numerical calculations of the multiphoton-transition cross sections are discussed. On the basis of the developed formalism the variation of the atomic spectrum in an intense field, the multiphoton ionization of atoms and the influence of the light field on electron-atom and atom-atom collision processes are examined.

Abstract: In this article we present a detailed overview of our studies of molecular photoionization and electron-molecule collisions in which we have used Schwinger-like variational principles and several important extensions of these principles. The various variational functionals and formulations, the interrelationships between these formulations, and a detailed discussion of the numerical and computational procedures which have been used in applications are presented.

Abstract: A survey is given of the current status of theoretical and experimental studies of elastic photon-atom scattering, with particular emphasis on the soft γ-ray energy regime 59.5 keV–1.33 MeV. Basic assumptions of theory, simple approximations, and best available calculations are described. The focus is on the Rayleigh scattering amplitudes for elastic scattering off the bound atomic electrons, but it is also necessary to discuss Delbruck and nuclear amplitudes. The numerical code of Kissel is central to the results which are obtained. A new reference data set of theoretical predictions is presented for a grid of 10 elements (Z = 13–103) and 7 energies (59.5 keV–1.33 MeV) at 55 scattering angles (0–180°). Basic considerations of the experiment are described, including sources and detectors and experimental arrangements. All modern experiments (using Ge detectors) are summarized, and older experiments are listed for reference. Finally, the status of comparison between theory and experiment is examined. All experiments available on the reference grid of theoretical calculation are compared with the predictions; agreement appears generally satisfactory. The situations at higher energies (focusing on Delbruck scattering) and lower energy X-ray scattering (anomalous scattering) are also discussed.

Abstract: A general formalism of parametric instabilities of electrostatic and electromagnetic waves in a magnetized plasma is presented. The Vlasov equation has been solved in the guiding center variables, incorporating the effects of finite wave number of pump, finite Larmor radius, resonant wave-particle interaction, and diamagnetic drift. In the limit of small Larmor radius, drift kinetic equation provides a simpler description. When applicable, fluid theory is used to yield a clearer physical picture. Only when the decay waves have wavelengths much shorter than that of the pump, the dipole pump ( k 0 = 0) approximation usually employed, is valid and the coupling coefficient, including full kinetic effects on the decay wa ves, is expressible in terms of electron and ion susceptibilities. The scheme adopted here is applicable to laboratory experiments as well as space plasma.

Abstract: The application of hydrodynamics to the study of heavy ion collisions is presented with emphasis on the relativistic regime. Current theoretical and experimental knowledge of the nuclear equations of state along with the possible roles played by viscosity, single- and double-shock waves and solitons during the collision are examined. Constraints imposed by relativity on the equation of state and numerical results from one- and three-dimensional one-fluid relativistic calculations are reviewed. Also considered are sources of entropy production arising from irreversible processes. Some alterations and additions to the basic equations of relativistic hydrodynamics are proposed to describe phenomena associated with relativistic heavy ion collisions. The equations of relativistic chromohydrodynamics are reviewed as a possible framework in which to consider the nuclear to quark-gluon phase transition. Transparency is introduced by a two-fluid model; results for center-of-mass bombarding energies up to 20 GeV per nucleon are presented. Recent work on pion production, the entropy problem and global analysis are reviewed.