"If there would be no God ~ then what a staff-captain am I?" ~ said one of the characters in a novel by Dostoevskii. In a similar way we can exclaim: "If there would be no nonlinearity ~ than what physics would that be'?". Really, the most interesting and exciting effects are described by non linear equations, and vanish in the linear approximation. For example, the general theory of relativity by A.Einstein comes to mind first - one of the most beautiful physical theories, which is in fact essentially nonlinear. Next, the phase transitions crystal ~ liquid and liquid ~ gas are due to the anhar monicity of inter-particle interactions, to dissociation and infinite motion. Similarly, transitions into the superconducting state or the superftuid would be impossible with purely harmonic interaction potentials. Another bril liant achievement in nonlinear physics was the construction of a laser and the subsequent development of nonlinear optics. The latter describes the in teraction of the matter with light of super-high intensity, when multi-quanta intra-molecular transitions become essential. Last, we should note here the very beautiful mathematical theory ~ the theory of catastrophes. Its subject is the study of invariant general properties of multi-dimensional surfaces in the vicinity of bifurcation points with respect to continuous transformations.

The Twenty-third Coral Gables conference on Unified Symmetry in the Small and in the Large was convened February 2-5, 1995. The shift of the traditional conference time from the last part of January was caused by the 1995 Superbowl's choice of our preferred date for their game. The conference was dedicated to reminiscences of Julian Schwinger. The death of Eugene P. Wigner in the early part of January 1995 was observed with a deep sorrow during the conference. At about that time the news of Asim Barut's death made 1995 an inauspicious year for physicists. In the meantime physics at the frontiers marched on as it did before. There were no path-breaking discoveries, but hope and persistence were still there. In 1964 (the first Coral Gables conference) if we had asked a physicist to give us a sincere opinion on what is "hot" in physics we would have expected him or her to point out the narrow area of their own research. The answer to this question in 1995 is still the same as it would have been in 1964. The mind set is a human quality and even in physics the physicist can respond like a religious believer.

For 75 years the stopping of energetic ions in matter has been a subject of great theoretical and experimental interest. The theoretical treatment of the stopping of ions in matter is largely due to the work of Bohr, 1-3 Bethe,4-6 Bloch,7. s and Lindhard,9-12 and it has been reviewed by Bohr,3 Fano,13 17 20 Jackson,14 Sigmund,15 Ahlen,16 and Ziegler et al. - Soon after the discovery of energetic particle emission from radioactive materials, there was interest in how these corpuscles were slowed down in traversing matter. In 1900, Marie Curie stated 21 the hypothesis that Hies rayons alpha sont des projectiles materiels susceptibles de perdre de leur vitesse en travers ant la matiere. " Early attempts to evaluate this were incon- clusive for there was not yet an accurate proposed model of the atom. Enough experimental evidence was collected in the next decade to make stopping power theory one of the central concerns of those attempting to develop an atomic model. J. J. Thomson, director of the prestigious Cavendish Laboratory, and Niels Bohr, a fresh postdoctoral scientist at Rutherford's Manchester Laboratory, both published almost simultaneously22. 23 an analysis of the stopping of charged particles by matter, and each contained many of their divergent ideas on the model of an atom. Thomson ignored in his paper the Rutherford alpha-particle scattering 24 experiment of a year before. But the nuclear atom with a heavy positively 25 charged core was the basis of Bohr's ideas.

From January 8-13,1990, distinguished physicists from many nations came to Chile to share with each other and with Latin American students exciting recent developments. The occasion was the third of a series of meetings on Quantum Mechanics of Fundamental Systems which are held every two years at the Centro de Estudios Cientificos de Santiago. This volume grew out from that gathering. The meeting was possible thanks to the generous support of the Tinker Foundation, the John D. and Catherine T. MacArthur Foundation, the International Centre for Theoretical Physics, the Ministere des AfIaires Etrangeres et Service Culturel et de Cooperation Scientifique et Technique de France, the Third World Academy of Sciences, and FONDECYT-Chile. The happy winds blowing over Chile at the time enhanced the joy provided by the beauty of the physics discussed. Claudio Teitelboim Jorge Zanelli Santiago, Chile vii Contents Chapter 1 Fractional Statistics in Quantum Mechanics Daniel P. Arovas 1. Introduction...1 2. Charge-Flux Composites...4 3. Dilute Anyon Gases ...6 4. Fractional Statistics in the Quantized Hall Effect ...8 5. Many-Body Theory of the Anyon Gas...16 6. Chern-Simons Field Theory and Fractional Statistics ...20 Appendix: Many Anyons in a Magnetic Field...23 . .

The present volume comprises the contributions of some of the participants of the NATO Advance Studies Institute "Turbulence, Weak and Strong", held in Cargese, in August 1994. More than 70 scientists, from seniors to young students, have joined to gether to discuss and review new (and not so new) ideas and developments in the study of turbulence. One of the objectives of the School was to incorporate, in the same meeting, two aspects of turbulence, which are obviously linked, and which are often treated sep arately: fully developed turbulence (in two and three dimensions) and weak turbulence (essentially one and two-dimensional systems). The idea of preparing a dictionary rather than ordinary proceedings started from the feeling that the terminology of turbulence includes many long, technical, poorly evocative words, which are usually not understood by people exterior to the field, and which might be worth explaining. Students who start working in the field of turbulence face a sort of curious situation: on one side, they are aware that turbulence is related to the disordered, churning flows of torrents, the pow erful movements of water in the oceans, the violent jet streams in the troposphere, the solar eruptions, and they are certainly excited to pierce the mystery of this fascinating, omnipresent phenomenon.

Reviews of Plasma Physics Volume 22, contains two reviews. The first Cooperative Effects in Plasmas by the late B.B. Kadomtsev is based on the second edition of the author's book in Russian which originated from his written lectures for students of the Moscow Institute of Physics and Technology. Kadomtsev intended to publish the book in English and even initiated the translation himself. The book represents a review of the typical plasma cooperative phenomena that determine the behavior of laboratory and astrophysical plasmas. It is characterized by lively language. The first three sections of the review deal with linear and nonlinear phenomena in fluids without a magnetic field. An additional subsection 'Solitons' has been added to the third section. The next two sections address regular nonlinear phenomena in a plasma in a magnetic field. The second review by S.V. Bulanov et al is connected with the contents of the first. The physics of the laser-plasma interaction including such nonlinear processes as wave breaking, the acceleration of charged particles, electromagnetic wave self-focusing, the relativistic soliton and vortex generation, are considered analytically and illustrated using computer simulations.

The material contained in this work concerns relativistic quantum mechanics, and as such pertains to classical fields. On the one hand it is meant to serve as a text on the subject, a desire stemming from the author's fruitless searches for an adequate, up-to-date reference when lecturing on these topics. At times the supplementary material was found to exceed by far that in the assigned text. On the other hand, there is some flavor of a monograph to what follows, most particularly in the later chapters, for a major goal is to demonstrate just how far we can advance our understanding of the behavior of stable particles and their interactions without introducing quantized fields. Those wishing to describe the world in this way may view the result as a point of departure, despite the fact that their wish remains unfulfilled. Confirmed quantum-field theorists, however, will doubtless view it as a summary of just why they feel compelled to quantize the fields. Approximately half the book is devoted to the single-particle Dirac equation and its solutions. A great deal of detail is provided in this respect, and the discus sion is reasonably comprehensive. The Dirac equation is extraordinarily important in its own right, particularly as a basis for quantum electrodynamics (QED), and is thus worthy of extensive study."

This volume contains the papers presented at the NATO Advanced Research Workshop on Localization and Propagation o[ Classical Waves in Random and Periodic Media held in Aghia Pelaghia, Heraklion, Crete, May 26- 30, 1992. The workshop's goal was to bring together theorists and experimentalists from two related areas, localization and photonic band gaps, to highlight their common interests. The objectives of the workshop were (i) to assess the state of-the-art in experimental and theoretical studies of structures exhibiting classical wave band gaps and/or localization, (ii) to discuss how such structures can be fabricated to improve technologies in different areas of physics and engineering, and (iii) to identify problems and set goals for further research. Studies of the propagation of electromagnetic (EM) waves in periodic and/or disordered dielectric structures (photonic band gap structures) have been and continue to be a dynamic area of research. Anderson localization of EM waves in disordered dielectric structures is of fundamental interest where the strong ei-ei interaction efFects entering the eIectron-localization are absent.

The XIV International Workshop on Condensed Matter Theories has been held at the Elba International Physics Center (EIPC), Marciana Marina, Isola d'Elba, Italy, from 18-23 June, 1990. The Workshop started in 1977 in Sao Paolo, Brazil, as the 1st Pan American Workshop on Condensed Matter Theories, with the purpose of bringing together scientists from the Western countries, working in many different topics of Condensed Matter Theories, to facilitate exchanges of ideas and technologies from different areas as well as collaborations among the scientists. The next five Workshops were held at Trieste, Italy (1978), in Buenos Aires, Argentina ( 1979), in Caracas, Venezuela (1980), in Mexico City, Mexico (1981) and in St. Louis, Missouri, U. S. A. (1982). Given the international dimension reached by the Workshop, it was decided to extend it into an International Workshop, which was held for the first time in Altenberg, Germany (1983). The next editions took place in Granada, Spain (1984), San Francisco, California, U. S. A. (1985), Argonne, Illinois, U. S. A. (1986), Oulu, Finland (1987), Taxco, Mexico (1988) and Campos do Jordao, Brasil (1989). Many scientists have contributed to the development of the various editions of the Work shop. However, a particular mention has to be made to Profs. Manuel de Llano and Angel Plastino who initially proposed the Workshop and carried it forward, and to Prof. J . W. Clark, whose efforts have been of immense help to its recent developments.

Numerous experiments and calculations have shown that isolated metal clusters possess many interesting features, quite different from those known from surface and solid- state physics or from atomic and molecular physics. The technological exploitation of these new properties, e.g. in miniature electronic or mechanical components, requires the cluster to be brought into an environment such as an encapsulating matrix or a surface. Due to the interaction with the contact medium, the properties of the clusters may change or even disappear. Thus the physics of cluster-on-surface systems -- the main subject of this book -- is of fundamental importance. The book addresses a wide audience, from the newcomer to the expert. Starting from fundamental concepts of adsorbate-surface interactions, the modification of electronic properties through electron confinement, and concepts of cluster production, it elucidates the distinct properties of the new metallic nanostructures.

The Editors have pleasure in presenting a further volume in the se ries to our international audience. Perhaps the most significant event of the passing year has been the publication by the IAEA of its study of the prob lem of continuing radiation protection in the lands surrounding Chernobyl. The major international project undertaken in 1990 and reported in 1991 is worth reading, not only for its assessment of how radiation protection intervention should be applied de facto in accident conditions, but equally for its account of the modern view of the philosophy of radiation protection. Some would, however, wish to argue that the acknowledgement by Iraq of its three-pronged development of nuclear weapons in conditions of secrecy and antagonism was equally significant and indeed as much a deter minant of the future of peaceful nuclear power as the Chernobyl accident. But it must be clear that the developments of weapons and electricity pro duction are not inescapably bound together; the Iraqi weapons program was not linked to any peaceful power development.

The recent discovery of a type II supernova in the Large Magellanic Cloud provides a rare chance to compare models of stellar evolution and nucleosynthesis directly with observations. This workshop covers thermonuclear reaction rates in chaos (experimental and theoretical), stellar evolution, nucleosynthesis and isotopic anomalies in meteorites and, in a final section, the supernovae, in particular SN 1987A. It brings the most interesting news in the rapidly developing field of nuclear astrophysics to researchers and also to graduate students. Recent and future developments are discussed. Special emphasis is placed on experimental and theoretical approaches to obtaining nuclear reaction rates, models of stellar evolution and explosions, and theories of nucleosynthesis. Various aspects of stellar evolution, nucleosynthesis, and thermonuclear reactions of astrophysical interest are reviewed. Several contributions deal with supernova explosions of massive stars, and in particular with Supernova 1987A and its impact on current models of the evolution of massive stars, the gravitational collapse of stellar cores, and neutrino physics and astronomy.

An understanding of the collisions between micro particles is of great importance for the number of fields belonging to physics, chemistry, astrophysics, biophysics etc. The present book, a theory for electron-atom and molecule collisions is developed using non-relativistic quantum mechanics in a systematic and lucid manner. The scattering theory is an essential part of the quantum mechanics course of all universities. During the last 30 years, the author has lectured on the topics presented in this book (collisions physics, photon-atom collisions, electron-atom and electron-molecule collisions, "electron-photon delayed coincidence technique", etc.) at many institutions including Wayne State University, Detroit, MI, The University of Western Ontario, Canada, and The Meerut University, India. The present book is the outcome of those lectures and is written to serve as a textbook for post-graduate and pre-PhD students and as a reference book for researchers.

The three articles of the present volume clearly exhibit a wide scope of articles, which is the aim of this series. The article by Kahana and Baltz lies in the main flow of the large stream of work currently in progress with heavy-ion accelerators. A related article by Terry Fortune on "Multinuclear Transfer Reactions with Heavy Ions" is scheduled to appear in the next volume. The article by Whitehead, Watt, Cole, and Morrison pertains to the nuclear-shell model for which a number of articles have appeared in our series. Our very first volume had an article on how SU(3) techniques can, with great elegance, enable one to cope with the sizable number of states within a configuration. But the actual nuclear force is not exactly that yielded by the elegant techniques, and so interest continued in dealing with the large number of states by brute force. Then the Glasgow school of Whitehead et al. discovered that mathematical techniques existed for coping more simply with the lowest eigenvalues of large matrices. The present ar ticle aims generally to make accessible to nuclear physicists the methods developed at Glasgow. The final article by Baer, Crowe, and Truol on radiative pion capture describes a new field of importance because of the advent of the meson factories. More and more pions and muons will become standard tools in nuclear physics."

This volume presents the proceedings of the Workshop on Momentum Distributions held on October 24 to 26, 1988 at Argonne National Laboratory. This workshop was motivated by the enormous progress within the past few years in both experimental and theoretical studies of momentum distributions, by the growing recognition of the importance of momentum distributions to the characterization of quantum many-body systems, and especially by the realization that momentum distribution studies have much in common across the entire range of modern physics. Accordingly, the workshop was unique in that it brought together researchers in nuclear physics, electronic systems, quantum fluids and solids, and particle physics to address the common elements of momentum distribution studies. The topics dis cussed in the workshop spanned more than ten orders of magnitude range in charac teristic energy scales. The workshop included an extraordinary variety of interactions from Coulombic to hard core repulsive, from non-relativistic to extreme relativistic."

Atomic Physics is certainly the oldest field in which Quantum Mechanics has been used and has provided the most significant proofs of this new theory. Most of the basic concepts, except those more recently developed in field quantization, have been understood for quite a time. Atomic Physics began to serve as a basis for other fields such as molecu lar, solid state or nuclear physics. A renewal of interest in Atomic Physics began in the sixties, after the discovery of Quantum Electro dynamics, and later when it provided some basic tests of fundamental questions like parity violation, time reversal or Dirac theory. More recently the development of new technologies led to the ex ploration of very extreme cases in which the most secrete aspects of atoms have been observed. - Rydberg states where the atoms are so big that they can be described by classical theories; - Heavy or super-heavy ions or exotic atoms where unknown QED or relativistic effects can be observed (very heavy hydrogenlike or helium like ions, positron production in very violent collisions **. ); - Huge external perturbations as those appearing in super-dense plasmas or ultra-high fields. The aim of this school was to gather atomic physicists from all over the world working in all these areas of Atomic Physics.

Seldom does a physical system, particularly one as apparently simple as the flow of a Newtonian fluid between concentric rotating cylinders, retain the interest of scientists, applied mathematicians and engineers for very long. Yet, as this volume goes to press it has been nearly 70 years since G. I. Taylor's outstanding experimental and theoretical study of the linear stability of this flow was published, and a century since the first experiments were performed on rotating cylinder viscometers. Since then, the study of this system has progressed enormously, but new features of the flow patterns are still being uncovered. Interesting variations on the basic system abound. Connections with open flows are being made. More complex fluids are used in some experiments. The vigor of the research going on in this particular example of nonequilibrium systems was very apparent at the NATO Advanced Research Workshop on "Ordered and Turbulent Patterns in Taylor Couette Flow," held in Columbus, Ohio, USA May 22-24, 1991. A primary goal of this ARW was to bring together those interested in pattern formation in the classic Taylor Couette problem with those looking at variations on the basic system and with those interested in related systems, in order to better define the interesting areas for the future, the open questions, and the features common (and not common) to closed and open systems. This volume contains many of the contributions presented during the workshop.

The mathematical technique of Monte Carlo, as applied to the transport of sub-atomic particles, has been described in numerous reports and books since its formal development in the 1940s. Most of these instructional efforts have been directed either at the mathematical basis of the technique or at its practical application as embodied in the several large, formal computer codes available for performing Monte Carlo transport calculations. This book attempts to fill what appears to be a gap in this Monte Carlo literature between the mathematics and the software. Thus, while the mathematical basis for Monte Carlo transport is covered in some detail, emphasis is placed on the application of the technique to the solution of practical radiation transport problems. This is done by using the PC as the basic teaching tool. This book assumes the reader has a knowledge of integral calculus, neutron transport theory, and Fortran programming. It also assumes the reader has available a PC with a Fortran compiler. Any PC of reasonable size should be adequate to reproduce the examples or solve the exercises contained herein. The authors believe it is important for the reader to execute these examples and exercises, and by doing so to become accomplished at preparing appropriate software for solving radiation transport problems using Monte Carlo. The step from the software described in this book to the use of production Monte Carlo codes should be straightforward.

Microcluster Physics provides a lucid account of the fundamental physics of all types of microclusters, outlining the dynamics and static properties of this new phase of matter intermediate between a solid and a molecule. Since originally published in 1991, the field of microclusters has experienced surprising developments, which are reviewed in this new edition: The determination of atomic structure, spontaneous alloying, super-shell, fission, fragmentation, evaporation, magnetism, fullerenes, nanotubes, atomic structure of large silicon clusters, superfluidity of a He cluster, water clusters in liquid, electron correlation and optimizsation of the geometry, and scattering.

Since the early days of modem physics spectroscopic techniques have been employed as a powerful tool to assess existing theoretical models and to uncover novel phenomena that promote the development of new concepts. Conventionally, the system to be probed is prepared in a well-defined state. Upon a controlled perturbation one measures then the spectrum of a single particle (electron, photon, etc.) emitted from the probe. The analysis of this single particle spectrum yields a wealth of important information on the properties of the system, such as optical and magnetic behaviour. Therefore, such analysis is nowadays a standard tool to investigate and characterize a variety of materials. However, it was clear at a very early stage that real physical compounds consist of many coupled particles that may be excited simultaneously in response to an external perturbation. Yet, the simultaneous (coincident) detection of two or more excited species proved to be a serious technical obstacle, in particular for extended electronic systems such as surfaces. In recent years, however, coincidence techniques have progressed so far as to image the multi-particle excitation spectrum in an impressive detail. Correspondingly, many-body theoretical concepts have been put forward to interpret the experimental findings and to direct future experimental research. This book gives a snapshot of the present status of multi-particle coincidence studies both from a theoretical and an experimental point of view. It also includes selected topical review articles that highlight the achievements and the power of coincident techniques.

The rivers run into the sea, yet the sea is not full Ecclesiastes What is quantum chemistry? The straightforward answer is that it is what quan tum chemists do. But it must be admitted, that in contrast to physicists and chemists, "quantum chemists" seem to be a rather ill-defined category of scientists. Quantum chemists are more or less physicists (basically theoreticians), more or less chemists, and by and large, computationists. But first and foremost, we, quantum chemists, are conscious beings. We may safely guess that quantum chemistry was one of the first areas in the natural sciences to lie on the boundaries of many disciplines. We may certainly claim that quantum chemists were the first to use computers for really large scale calculations. The scope of the problems which quantum chemistry wishes to answer and which, by its unique nature, only quantum chemistry can answer is growing daily. Retrospectively we may guess that many of those problems meet a daily need, or are say, technical in some sense. The rest are fundamental or conceptual. The daily life of most quantum chemists is usually filled with grasping the more or less technical problems. But it is at least as important to devote some time to the other kind of problems whose solution will open up new perspectives for both quantum chemistry itself and for the natural sciences in general.

The present volume contains the text of the invited talks delivered at the Eighth International Conference on Recent Progress in Many-Body Theories held at SchloB Seggau, Province of Styria, Austria, during the period August 22-26, 1994. The pro ceedings of the Fifth Conference (Oulu, Finland 1987), the Sixth Conference (Arad, Israel 1989) and the Seventh Conference (Minneapolis, USA 1991) have been published. by Plenum as the first three volumes of this series. Papers from the First Conference (Trieste, Italy 1978) comprise Nuclear Physics volume A328, Nos. 1 and 2, the Second Conference (Oaxtepec, Mexico 1979) was published by Springer-Verlag as volume 142 of "Lecture Notes in Physics," entitled "Recent Progress in Many Body Theories." Vol ume 198 of the same series contains the papers from the Third Conference (Altenberg, 1983). These volumes intend to cover a broad spectrum of current research topics in physics that benefit from the application of many-body theories for their elucidation. At the same time there is a focus on the development and refinement of many-body methods. One of the major aims of the conference series has been to foster the exchange of ideas among physicists working in such diverse areas as nuclear physics, quantum chemistry, complex systems, lattice Hamiltonians, quantum fluids and condensed matter physics. The present volume contains contributions from all these areas. th The conference was dedicated on the occasion of Ludwig Boltzmann's 150 birthday."

Topological defects have recently become of great interest in condensed matter physics, particle physics and cosmology. They are the unavoidable remnants of many symmetry breaking phase transitions. Topological defects can play an important role in describing the properties of many condensed matter systems (e.g. superfluids and superconduc tors); they can catalyze many unusual effects in particle physics models and they may be responsible for seeding the density perturbations in the early Universe which de velop into galaxies and the large-scale structure of the Universe. Topological defects are also of great interest in mathematics as nontrivial solutions of nonlinear differential equations stabilized by topological effects. The purpose of the Advanced Study Institute "Formation and Interactions of Topo logical Defects" was to bring together students and practitioners in condensed matter physics, particle physics and cosmology, to give a detailed exposition of the role of topo logical defects in these fields; to explore similarities and differences in the approaches; and to provide a common basis for discussion and future collaborative research on common problems.