Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary variables. The use of density matrix methods also has the advan tage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incompletely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics."

Experimental Metaphysics is intended for theoretical physicists and philosophers of science and is devoted to fundamental issues in the quantum domain. The book presents a number of discussions of experiments, theoretical puzzles and alternative interpretations, and philosophical treatments of the metaphysical foundations of science and the way these throw a scientific light on metaphysics. Hence the title: experimental metaphysics' is a term coined by Abner Shimony, to whom the book is dedicated. This collection of 16 scientific and philosophical essays by leading physicists, philosophers and historians of science deals with current research and the most basic issues in quantum physics.

In this volume we aim to introduce recent progress in the study of aperiodic materials, which include icosahedral clusters, amorphous metals, quasicrys- tals, glasses, and liquids. Quasicrystals, discovered in 1984, correspond to a kind of revolution in our understanding of crystallography, wherein the five-fold rotational symmetry was prohibited in long-range ordered systems. Various interesting physicochemical properties of these materials strongly depend on structural inhomogeneity at the microscopic level, and the small angle X-ray scattering method is widely used to analyze such structures. These new materials provide fundamental improvements to materials prop- erties, and are not only scientifically interesting but also industrially impor- tant for applications such as ultrafine magnetic recording media and future electronic devices. This book contains three chapters. The first chapter, written by H. Tanaka and T. Fujiwara, deals with 'Electronic Structure in Aperiodic Materials', and reviews the application of theoretical methods to determine the elec- tronic structures and resulting properties of amorphous metals, quasicrys- tals, and liquids. The second chapter, written by Y. Waseda, K. Sugiyama, and A. H. Shinohara, covers the recent topic of 'Anomalous Small Angle X- ray Scattering for Structural Inhomogeneity of Materials', starting with its fundamentals. The third chapter, 'Icosahedral Clusters in RE(TM - Al h3 1 x x Amorphous Alloys', by K. Fukamichi, A. Fujita, T. H. Chang, E. Matsubara, and Y.

This book contains comprehensive reviews of modern topics in nuclear physics, particle physics, astrophysics and cosmology. Special emphasis is placed on the role of several symmetries in physics at intermediate and high energies and on neutrino physics, with its implications in nuclear astrophysics and cosmology.
Many applications of the theories and experiments are included, along with interesting information on recent developments with respect to current problems in modern physics. Thus, it will be especially useful to new scientists and graduate students.

Explicitly Correlated Wave Functions in Chemistry and Physics is the first book devoted entirely to explicitly correlated wave functions and their theory and applications in chemistry and molecular and atomic physics. Explicitly correlated wave functions are functions that depend explicitly on interelectronic distance.
The book covers a wide range of methods based on explicitly correlated functions written by leaders in the field, including Kutzelnigg, Jeziorski, Szalewicz, Klopper and Noga. The book begins with a chapter on the theory of electron correlation and then the following three chapters describe different types of functions that can be used to solve the electronic Schrodinger equation for atoms and molecules. The book goes on to discuss the effects that go beyond the Born-Oppenheimer approximation, theory of relativistic effects, solution of the Dirac-Colomb equation, and relativistic correction using ECG functions. The last part of the book reviews applications of EC functions to calculate atomic and molecular properties and to study positronic systems, resonance states of atoms and nuclear dynamics of the hydrogen molecular ion.
"

Surfaces and interfaces play an increasingly important role in today's solid state devices. In this book the reader is introduced, in a didactic manner, to the essential theoretical aspects of the atomic and electronic structure of surfaces and interfaces. The book does not pretend to give a complete overview of contemporary problems and methods. Instead, the authors strive to provide simple but qualitatively useful arguments that apply to a wide variety of cases. The emphasis of the book is on semiconductor surfaces and interfaces but it also includes a thorough treatment of transition metals, a general discussion of phonon dispersion curves, and examples of large computational calculations. The exercises accompanying every chapter will be of great benefit to the student.

Quantum mechanics does away with the distinction between particles and waves, and one of the more interesting implications of the wave/particle duality - the discovery that atoms may be manipulated in ways analogous to the manipulation of light with lenses and mirrors - has formed the basis for the relatively new field of atom optics. Pierre Meystre's Atom Optics is the first book entirely devoted to this exciting area of research. Reference links to the leading journals in the field, links to research sites, graphics, and updates can be found online.

Fullerene Collision Reactions provides a comprehensive overview of the state-of-the-art of fullerene collision studies. The book begins with introductory chapters that provide the necessary background in experimental and theoretical techniques. This is followed by experimental results and theoretical calculations covering the wide range of available gas-phase fullerene collision experiments.
Emphasis is placed on gas-phase molecular beam experiments where reaction, fragmentation and charge transfer cross sections have been determined covering collision energy ranges from thermal to MeV. Atomic, ionic, electronic, cluster and surface collisions involving fullerenes are covered in depth accompanied by a clear presentation of the most commonly applied experimental and theoretical techniques.
This book will be an invaluable resource for senior undergraduate students, graduate students and researchers working in the field.

Progress in atomic physics has been so vigorous during the past decade that one is hard pressed to follow all the new developments. In the early 1990s the first atom interferometers opened a new field in which we have been able to use the wave nature of atoms to probe fundamental quantum me chanics questions as well as to make precision measurements. Coming fast on the heels of this development was the demonstration of Bose Einstein condensation in dilute atomic vapors which intensified research interest in studying the wave nature of matter, especially in a domain in which "macro scopic" quantum effects (vortices, stimulated scattering of atomic beams) are visible. At the same time there has been much progress in our understanding of the behavior of waves (notably electromagnetic) in complex media, both periodic and disordered. An obvious topic of speculation and probably of future research is whether any new insight or applications will develop if one examines the behavior of de Broglie waves in analogous situations. Finally, our ability to manipulate atoms has allowed us not only to create macroscopically occupied quantum states but also to exercise fine control over the quantum states of a small number of atoms. This has advanced to the study of quantum entanglement and its relation to the theory of measurement and the theory of information. The 1990s have also seen an explosion of interest in an exciting potential application of this fine control: quantum computation and quantum cryptography.

This monograph is the fIrst book exclusively devoted to Dusty and Dirty from a unifIed Electrohydrodynamical point of view, incorporating new Plasmas concepts of Electric Cusp-Reconnection and Generalized Critical Ionization Velocities, based on a survey stimulated from a series of International Wo- shops/Symposia on Plasmas in Space and in the Laboratory held in Tokyo since 1980, and from associations with a number of Universities and Institutions which offered me opportunities to do specifIc research. For example, the subjects of Mirrors and Cusps, Critical Velocities, Double Layers or Dipoles, and Quadrupoles in this monograph were initiated by the fIrst International Workshop on Relation between Laboratory and Space Plasmas held in Tokyo in 1980 which was well received, in this connection in particular thankfully by the late Professor Hannes Alfven with encouraging communica tions, inspiring me to studies of critical velocities, electrical version offield line merging-reconnection, and Unconventional Plasmas. Although the subject of this monograph was partly included also in topics at the URSI Workshop on Nonlinear and Environmental Electromagnetics in 1984, at the second Wo- shop on Relation between Laboratory and Space Plasmas in 1986, and at the URSI Symposium on Environmental and Space Electromagnetics in 1989, the main subject: Dusty and Dirty Plasmas and EHD (electrohydrodynamics) was discussed exclusively at the later Symposium in 1992, resulting in the fIrst monograph, Dusty and Dirty Plasmas with Noise and Chaos in Space and in the Laboratory in this fIeld for which Professor John E.

Polarization Spectroscopy of Ionized Gases describes the physical principles of the technique and its applications to remote sensing. Transport phenomena and local anisotropies can be studied. The theoretical part of the book considers the basic phenomena of the ordering of the velocities of fast exciting charged particles. The polarization of the outer electron shells of excited atoms or molecules is described, and a variety of effects are examined in detail. An integral equation is derived which gives the intensity and polarization of emitted lines. Methods for solving the equation are analyzed. Universal spectropolarimetric remote sensing has been applied to low pressure gas discharges in the laboratory and to non-thermal processes in the solar atmosphere. For researchers interested in the remote sensing of ionized gases.

Focused on basic science, this book reviews experiments on metal clusters in two long pedagogically written articles. Interested readers will also find articles ranging from density functional theory to computer simulations of cluster dynamics.

The development of advanced materials with preselected properties is one of the main goals of materials research. Of especial interest are electronics, high-temperature and supemard materials for various applications, as well as alloys with improved wear, corrosion and mechanical resistance properties. The technical challenge connected with the production of these materials is not only associated with the development of new specialised preparation techniques but also with quality control. The energetic charged particle, electron and photon beams offer the possibility of modifying the properties of the near-surface regions of materials without seriously affecting their bulk, and provide unique analytical tools for testing their qUality. This volume includes most of the lectures and contributions delivered at the NATO-funded Advanced Study Institute "Application of Particle and Laser Beams in Materials Technology," which was held in Kallithea, Chalkidiki, in Northern Greece, from the 8th to the 21st of May, 1994 and attended by 73 participants from 21 countries. The aim of this ASI was to provide to the participants an overview of this rapidly expanding field. Fundamental aspects concerning the interactions and collisions on atomic, nuclear and solid state scale were presented in a didactic way, along with the application of a variety of techniques for the solution of problems ranging from the development of electronics materials to corrosion research and from archaeometry to environmental protection.

These two volumes constitute the Proceedings of the Conference Moshe Flato, 1999'. Their spectrum is wide but the various areas covered are, in fact, strongly interwoven by a common denominator, the unique personality and creativity of the scientist in whose honor the Conference was held, and the far-reaching vision that underlies his scientific activity. With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics. Volume I is prefaced by reminiscences of and tributes to Flato's life and work. It also includes a section on the applications of sciences to insurance and finance, an area which was of interest to Flato before it became fashionable. The bulk of both volumes is on physical mathematics, where the reader will find these ingredients in various combinations, fundamental mathematical developments based on them, and challenging interpretations of physical phenomena. Audience: These volumes will be of interest to researchers and graduate students in a variety of domains, ranging from abstract mathematics to theoretical physics and other applications. Some parts will be accessible to proficient undergraduate students, and even to persons with a minimum of scientific knowledge but enough curiosity.

Quantum mechanics provides the fundamental theoretical apparatus for describing the structure and properties of atoms and molecules in terms of the behaviour of their fundamental components, electrons and nudeL For heavy atoms and molecules containing them, the electrons can move at speeds which represent a substantial fraction of the speed of light, and thus relativity must be taken into account. Relativistic quantum mechanics therefore provides the basic formalism for calculating the properties of heavy-atom systems. The purpose of this book is to provide a detailed description of the application of relativistic quantum mechanics to the many-body prob lem in the theoretical chemistry and physics of heavy and superheavy elements. Recent years have witnessed a continued and growing interest in relativistic quantum chemical methods and the associated computa tional algorithms which facilitate their application. This interest is fu elled by the need to develop robust, yet efficient theoretical approaches, together with efficient algorithms, which can be applied to atoms in the lower part of the Periodic Table and, more particularly, molecules and molecular entities containing such atoms. Such relativistic theories and computational algorithms are an essential ingredient for the description of heavy element chemistry, becoming even more important in the case of superheavy elements. They are destined to become an indispensable tool in the quantum chemist's armoury. Indeed, since relativity influences the structure of every atom in the Periodic Table, relativistic molecular structure methods may replace in many applications the non-relativistic techniques widely used in contemporary research."

Hydrogen bonds represent type of molecular interaction that determines the structure and function of a large variety of molecular systems. The elementary dynamics of hydrogen bonds and related proton transfer reactions, both occurring in the ultra fast time domain between 10-14 and 10-11s, form a research topic of high current interest.
In this book addressing scientists and graduate students in physics, chemistry and biology, the ultra fast dynamics of hydrogen bonds and proton transfer in the condensed phase are reviewed by leading scientists, documenting the state of the art in this exciting field from the viewpoint of theory and experiment. The nonequilibrium behavior of hydrogen-bonded liquids and intramolecular hydrogen bonds as well as photo induced hydrogen and proton transfer are covered in 7 chapters, making reference to the most recent literature.

The last decade witnessed an increasing interest of mathematicians in prob lems originated in mathematical physics. As a result of this effort, the scope of traditional mathematical physics changed considerably. New problems es pecially those connected with quantum physics make use of new ideas and methods. Together with classical and functional analysis, methods from dif ferential geometry and Lie algebras, the theory of group representation, and even topology and algebraic geometry became efficient tools of mathematical physics. On the other hand, the problems tackled in mathematical physics helped to formulate new, purely mathematical, theorems. This important development must obviously influence the contemporary mathematical literature, especially the review articles and monographs. A considerable number of books and articles appeared, reflecting to some extend this trend. In our view, however, an adequate language and appropriate methodology has not been developed yet. Nowadays, the current literature includes either mathematical monographs occasionally using physical terms, or books on theoretical physics focused on the mathematical apparatus. We hold the opinion that the traditional mathematical language of lem mas and theorems is not appropriate for the contemporary writing on mathe matical physics. In such literature, in contrast to the standard approaches of theoretical physics, the mathematical ideology must be utmost emphasized and the reference to physical ideas must be supported by appropriate mathe matical statements. Of special importance are the results and methods that have been developed in this way for the first time."

Remarkable recent progress in quantum optics has given rise to extremely precise quantum measurements that are used in the research into the fundamentals of quantum physics, and in different branches of physics such as optical spectroscopy. This progress stimulates new technologies in the field of optical communications, optical computation and information systems. This state-of-the-art volume presents work from a Summer School on Advances in Quantum Optics and Spectroscopy of Solids, held in Ankara, Turkey, in 1995. The various contributions written by leading scientists in the field cover a wide range of subjects in this exciting area of physics, and report new and important results and ideas. Topics dealt with include the interaction of quantum light with trapped atoms and condensed matter; quantum tomography and phase analysis; and many applications of quantum optics from mesoscopic physics to correlation spectroscopy of non-classical states, which are of major importance in understanding the nature of collective excitations in solids. Audience: This book will be of interest to postgraduate students and researchers whose work involves quantum optics, solid state spectroscopy and its applications.

This is the third Selecta of publications of Elliott Lieb, the first two being Stabil ity of Matter: From Atoms to Stars, edited by Walter Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai. A companion fourth Selecta on Statistical Mechanics is also edited by us. Elliott Lieb has been a pioneer of the discipline of mathematical physics as it is nowadays understood and continues to lead several of its most active directions today. For the first part of this selecta we have made a selection of Lieb's works on Condensed Matter Physics. The impact of Lieb's work in mathematical con densed matter physics is unrivaled. It is fair to say that if one were to name a founding father of the field, Elliott Lieb would be the only candidate to claim this singular position. While in related fields, such as Statistical Mechanics and Atomic Physics, many key problems are readily formulated in unambiguous mathematical form, this is less so in Condensed Matter Physics, where some say that rigor is "probably impossible and certainly unnecessary." By carefully select ing the most important questions and formulating them as well-defined mathemat ical problems, and then solving a good number of them, Lieb has demonstrated the quoted opinion to be erroneous on both counts. What is true, however, is that many of these problems turn out to be very hard. It is not unusual that they take a decade (even several decades) to solve."

Sonochemistry is studied primarily by chemists and sonoluminescence mainly by physicists, but a single physical phenomenon - acoustic cavitation - unites the two areas. The physics of cavitation bubble collapse, is relatively well understood by acoustical physicists but remains practically unknown to the chemists. By contrast, the chemistry that gives rise to electromagnetic emissions and the acceleration of chemical reactions is familiar to chemists, but practically unknown to acoustical physicists. It is just this knowledge gap that the present volume addresses. The first section of the book addresses the fundamentals of cavitation, leading to a more extensive discussion of the fundamentals of cavitation bubble dynamics in section two. A section on single bubble sonoluminescence follows. The two following sections address the new scientific discipline of sonochemistry, and the volume concludes with a section giving detailed descriptions of the applications of sonochemistry. The mixture of tutorial lectures and detailed research articles means that the book can serve as an introduction as well as a comprehensive and detailed review of these two interesting and topical subjects.

Relativity plays an important role in atomic nuclei, and, since the early 1970s, there has been increasing interest in, and literature on, the nucleus as a relativistic system. In fact, the relativistic treatment provides a powerful method to describe nuclear structure and reactions. It is thus an ideal time to collect and review the important landmarks in this book. Directed to advanced students and researchers, it explains both the underlying relativistic theory and compares predictions with actual experiments.

The importance of the Vavilov-Cherenkov radiation stems from the property that a charge moving uniformly in a medium emits ? quanta at the angle uniquely related to its energy. This has numerous applications. We mention only the neutrino experiments in which the neutrino energy is estimated by the angle at which the electron originating from the decay of neutrino is observed. This book is intended for students of the third year and higher, for postgraduates, and professional scientists, both experimentalists and th- reticians. The Landau and Lifschitz treatisesQuantumMechanics,Clas- cal Field Theory andElectrodynamicsofContinuousMedia are more than enough for the understanding of the text. There are three monographs devoted to the Vavilov-Cherenkov rad- tion. Jelly's book Cherenkov Radiation and its Applications published in 1958 contains a short theoretical review of the Vavilov-Cherenkov ra- ation and a rather extensive description of experimental technique. Ten years later, the two-volume Zrelov monograph Vavilov-Cherenkov Rad- tionandItsApplicationinHigh-EnergyPhysics appeared. Its ?rst volume isaquiteextensivereviewofexperimentalandtheoreticalresultsknownup to1968.ThesecondvolumeisdevotedtotheconstructionoftheCherenkov counters. In1988,theFrankmonographVavilov-CherenkovRadiation.T- oretical Aspects was published. It presents mainly a collection of Frank's papers with valuable short commentaries describing their present status. It is highly desirable to translate this book into English.

The workshop on The Cosmology of Extra Dimensions and Varying Fundamental Constants, which was part of JENAM 2002, was held at the Physics Department of the University of Porto (FCUP) from the 3rd to the 5th of September 2002. It was regularly attended by about 110 participants, of which 65 were officially registered in the VFC workshop, while the others came from the rest of the JENAM workshops. There were also a few science correspondents from the national and international press. During the 3 days of the scientific programme, 8 Invited Reviews and 30 Oral Communications were presented. The speakers came from 11 different European countries, and also from Argentina, Australia, Canada, Japan and the U.S.A. There were also speakers from six Portuguese research institutions, and nine of the speak ers were Ph.D. students. The contributions are presented in these proceedings in chronological order. The workshop brought together string theorists, particle physicists, theoretical and observational cosmologists, relativists and observational astrophysicists. It was generally agreed that this inter-disciplinarity was the greatest strength of the work shop, since it provided people coming into this very recent topic from the various different backgrounds with an opportunity to understand each other's language and thereby gain a more solid understanding of the overall picture."

Biomedical EPR Part B focuses on applications of EPR techniques and instrumentation, with applications to dynamics. The book celebrates the 70th birthday of Prof. James S. Hyde, Medical College of Wisconsin, and his contributions to this field. Chapters are written to provide introductory material for new-comers to the field that lead into up-to-date reviews that provide perspective on the wide range of questions that can be addressed by EPR.

Key Features:
EPR Techniques including Saturation Recovery, ENDOR, ELDOR, and Saturation Transfer

Instrumentation Innovations including Loop Gap Resonators, Rapid Mixing, and Time Locked Sub-Sampling

Motion in Biological Membranes

Applications to Structure Determination in Proteins

Discussion of Trends in EPR Technology and Prognosis for the Future "

There is a unity to physics; it is a discipline which provides the most fundamental understanding of the dynamics of matter and energy. To understand anything about a physical system you have to interact with it and one of the best ways to learn something is to use electrons as probes. This book is the result of a meeting, which took place in Magdalene College Cambridge in December 2001. Atomic, nuclear, cluster, soHd state, chemical and even bio- physicists got together to consider scattering electrons to explore matter in all its forms. Theory and experiment were represented in about equal measure. It was meeting marked by the most lively of discussions and the free exchange of ideas. We all learnt a lot. The Editors are grateful to EPSRC through its Collaborative Computational Project program (CCP2), lOPP, the Division of Atomic, Molecular, Optical and Plasma Physics (DAMOPP) and the Atomic Molecular Interactions group (AMIG) of the Institute of Physics for financial support. The smooth running of the meeting was enormously facilitated by the efficiency and helpfulness of the staff of Magdalene College, for which we are extremely grateful. This meeting marked the end for one of us (CTW) of a ten-year period as a fellow of the College and he would like to take this opportunity to thank the fellows and staff for the privilege of working with them.