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TIlis volume contains the contributions to the Euromech Colloquium No. 241 on Nonlinear Waves in Active Media at the Institute of Cybernetics of the Estonian Academy of Sciences, Tallinn, Estonia, USSR, September 27-30, 1988. The Co-chairmen of the Euromech Colloquium felt that it would be a good service to the community to publish these proceedings. First, the topic itself dealing with various wave processes with energy influx is extremely interesting and attracted a much larger number of participants than usual - a clear sign of its importance to the scientific community. Second, Euromech No. 241 was actually the first Euromech Colloquium held in the Soviet Union and could thus be viewed as a milestone in the extending scientific contacts between East and West. At the colloquium 50 researchers working in very different branches of sci­ ence met to lecture on their results and to discuss problems of common interest. An introductory paper by I. Engelbrecht presents the common motivation and background of the topics covered. Altogether 36 speakers presented their lectures, of which 30 are gathered here. The remaining six papers which will appear elsewhere are listed on page X. In addition, three contributions by authors who could not attend the colloquium are included. The two lectures given by A.S. Mikhailov, V.S. Davydov and V.S. Zykov are here published as one long paper.

The great advantage of coincidence measurements is that by suitable choice of the kinematical and geometrical arrangement one may probe delicate physical effects which would be swamped in less differential experiments. The measurement of the triple dif­ ferential and higher-order cross sections presents enormous technical difficulties, but refined experiments of this type provide an insight into the subtleties of the scattering process and offer a welcome, if severe, test of the available theoretical models. The last few years have been an exciting time to work in the field and much has been learned. Profound insights have been gleaned into the basic Coulomb few body problem in atomic physics: the experimental study of the fundamental (e,2e) processes on hydrogen and helium targets continues to add to our knowledge and indeed to challenge the best of our theoretical models; significant advances have been made in the understanding of the'double excitation problem,'that is the study of ionization processes with two active target electrons: important measurements of (e,3e), (,),,2e), excitation-ionization and excitation autoionization have been reported and strides have been made in their theoretical description; the longstanding discrepancies between theory and experiment for relativistic (e,2e) processes were resolved, spin dependent effects predicted and ob­ served and the first successful coincidence experiments on surfaces and thin films were announced. Theory and experiment have advanced in close consort. The papers pre­ sented here cover the whole gambit of research in the field. Much has been achieved but much remains to be done.

The last few years have seen some remarkable advances in the understanding of atomic phenomena. It is now possible to isolate atomic systems in traps, measure in coincidence the fragments of collision processes, routinely produce, and study multicharged ions. One can look at bulk matter in such a way that the fundamental atomic character is clearly evident and work has begun to tease out the properties of anti­ matter. The papers in this book reflect many aspects of modem Atomic Physics. They correspond to the invited talks at a conference dedicated to the study of'New Directions in Atomic Physics,'which took place in Magdalene College, Cambridge in July of 1998. The meeting was designed as a way of taking stock of what has been achieved and, it was hoped, as a means of stimulating new research in new areas, along new lines. Consequently, an effort was made to touch on as many directions as we could in the four days of the meeting. We included some talks which overviewed whole subfields, as well as quite a large number of research contributions. There is a unity to Physics and we tried to avoid any artificial division between theory and experiment. We had roughly the same number of talks from those who are primarily concerned with making measurements, and from those who spend their lives trying to develop the theory to describe the experiments.

Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet scientists working in this field. Instead of producing for the first time English proceedings it has been decided to present a good cross section of nonlinear physics in the USSR. Thus the participants at the last School were invited to provide English reviews and research papers for these two volumes (which in the years to come will be followed by the proceedings of forthcoming schools). The second volume deals with dynamical chaos in classical and quantum systems, with evolution in chemical systems and self-organisation in biology, and with applications of nonlinear dynamics to condensed matter, sea waves, and astrophysics.

Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet scientists working in this field. Instead of producing for the first time English proceedings it has been decided to present a good cross section of nonlinear physics in the USSR. Thus the participants at the last School were invited to provide English reviews and research papers for these two volumes (which in the years to come will be followed by the proceedings of forthcoming schools). The first volume starts with a historical overview of nonlinear dynamics from Poincaré to the present day and touches topics like attractors, nonlinear oscillators and waves, turbulence, pattern formation, and dynamics of structures in nonequilibrium dissipative media. It then deals with structures, bistabilities, instabilities, chaos, dynamics of defects in 1d systems, self-organizations, solitons, spatio-temporal structures and wave collapse in optical systems, lasers, plasmas, reaction-diffusion systems and solids.

Time and quantum mechanics have, each of them separately, captivated s- entists and laymen alike, as shown by the abundance of popular publications on “time” or on the many quantum mysteries or paradoxes. We too have been seduced by these two topics, and in particular by their combination. Indeed, the treatment of time in quantum mechanics is one of the important and challenging open questions in the foundations of quantum theory. This book describes the problems, and the attempts and achievements in de?ning, formalizing and measuring di?erent time quantities in quantum theory, such as the parametric (clock) time, tunneling times, decay times, dwell times, delay times, arrival times or jump times. The theoretical analysis of several of these quantities has been controversial and is still subject to debate. For example, there are literally hundreds of research papers on the tunneling time. In fact, the standard recipe to link the observables and the formalism does not seem to apply, at least in an obvious manner, to time observables. This has posed the challenge of extending the domain of ordinary quantum mechanics.

This expert and self-contained authored handbook provides comprehensive coverage of liquid crystals from the fundamental materials science, physics, and modeling through cutting-edge applications. Written by an author with over 40 years of active experience in this growing field, it offers an unprecedented self-contained treatment of this key research area.Liquid Crystals are a state of matter sharing properties that are usually associated with both solids and liquids. Their study belongs to wider field of soft condensed matter physics, an area growing in importance because of the new physics being discovered and the possibilities of various technological applications being developed. Liquid crystals continue to have a revolutionary technological impact and consistently pose new challenges of basic understanding. While the experimental side of liquid crystal research is very well developed, theoretical understanding has lagged, and this volume fills a gap in the published literature in terms of rigorous treatment of mathematical and computer modeling approaches.Volume II of this handbook deals with advanced aspects of liquid crystals and their applications, covering computer simulations of phase transitions in liquid crystals, liquid crystals of biomolecules, and defect textures in liquid crystals. Overall, this handbook serves as the ultimate scholarly guide for researchers, scientists, and engineers seeking to unlock the full potential of liquid crystals. It offers a comprehensive understanding of these materials and their diverse applications, empowering readers to navigate the complex intricacies of liquid crystal science and technology.

This second edition adds 46 new problems, for a total of 203. The solutions to certain “old” problems have been revised for improved clarity, in response to questions and comments from our students (second-year students in the Master's in Physics program). Each problem is given a title indicating its relation to the various areas of physics or technology. By tackling the problems presented here, students are gently introduced to advanced topics such as unipolar and homopolar motors, magnetic monopoles, radiation pressure, angular momentum of light, bulk and surface plasmons, and radiation friction. We also address a number of tricky concepts and apparent ambiguities and paradoxes encountered in the classical theory of electromagnetism, with a particular focus on conservation laws and transformation properties between different frames of reference. At the same time, the book can be used as an introduction to applications of classical electromagnetism including cutting-edge topics like plasmonics, metamaterials, and light-driven propulsion. While unnecessary mathematical complexity is avoided, the new edition also provides a few introductory examples concerning elegant and powerful solution techniques. Hopefully the second edition offers an even better teaching tool for undergraduates in physics, mathematics, and electric engineering, and a valuable reference guide for students planning to work in optics, material science, electronics, and plasma physics.

This thesis establishes a multifaceted extension of the deterministic control framework that has been a workhorse of nonequilibrium statistical mechanics, to stochastic, discrete, and autonomous control mechanisms. This facilitates the application of ideas from stochastic thermodynamics to the understanding of molecular machines in nanotechnology and in living things. It also gives a scale on which to evaluate the nonequilibrium energetic efficiency of molecular machines, guidelines for designing effective synthetic machines, and a perspective on the engineering principles that govern efficient microscopic energy transduction far from equilibrium. The thesis also documents the author's design, analysis, and interpretation of the first experimental demonstration of the utility of this generally applicable method for designing energetically-efficient control in biomolecules. Protocols designed using this framework systematically reduced dissipation, when compared to naive protocols, in DNA hairpins across a wide range of experimental unfolding speeds and between sequences with wildly different physical characteristics.

In two volumes, this book presents a detailed, systematic treatment of electromagnetics with application to the propagation of transient electromagnetic fields (including ultrawideband signals and ultrashort pulses) in dispersive absorptive media. This expanded, updated, and reorganized new edition presents a rigorous development of both time- and frequency-domain electromagnetics, from classical theory to current topics in applied research on temporally pulsed wave fields in dielectric, conducting, and semiconducting materials. With meaningful exercises throughout, it is suitable as a graduate textbook in electromagnetic wave theory and will be of use to researchers as a resource on electromagnetic radiation and wave propagation theory with applications to radar, imaging, communications, and safety issues.Volume 1 develops the fundamental Maxwell-Lorentz theory of microscopic electromagnetics and its relationship to macroscopic electromagnetics in complex media with particularemphasis given to temporally dispersive materials, supplemented with several appendices on mathematical methods. The second edition includes new material on conjugate electromagnetic fields, time-reversal invariance, the four-potential and Lorentz invariance, anisotropic and spatially dispersive media, double-negative metamaterials, and generalized Fresnel reflection and refraction coefficients for complex media. The relationship between both the mathematical and physical interpretation of classical electromagnetic field theory with the special theory of relativity is emphasized throughout the volume. Volume 2 covers temporal pulse dynamics in dispersive attenuative media, with asymptotic analysis at the forefront.

In two volumes, this book presents a detailed, systematic treatment of electromagnetics with application to the propagation of transient electromagnetic fields (including ultrawideband signals and ultrashort pulses) in dispersive attenuative media. The development in this expanded, updated, and reorganized new edition is mathematically rigorous, progressing from classical theory to the asymptotic description of pulsed wave fields in Debye and Lorentz model dielectrics, Drude model conductors, and composite model semiconductors. It will be of use to researchers as a resource on electromagnetic radiation and wave propagation theory with applications to ground and foliage penetrating radar, medical imaging, communications, and safety issues associated with ultrawideband pulsed fields. With meaningful exercises, and an authoritative selection of topics, it can also be used as a textbook to prepare graduate students for research. Volume 2 presents a detailed asymptotic description of plane wave pulse propagation in dielectric, conducting, and semiconducting materials as described by the classical Lorentz model of dielectric resonance, the Rocard-Powles-Debye model of orientational polarization, and the Drude model of metals. The rigorous description of the signal velocity of a pulse in a dispersive material is presented in connection with the question of superluminal pulse propagation. The second edition contains new material on the effects of spatial dispersion on precursor formation, and pulse transmission into a dispersive half space and into multilayered media. Volume 1 covers spectral representations in temporally dispersive media.

This book discusses the electromagnetic response function of matter, providing a logically more complete form of macroscopic Maxwell equations than the conventional literature. It shows that various problems inherent to the conventional macroscopic Maxwell equations are solved by the first-principles derivation presented. Applying long wavelength approximation to microscopic nonlocal response theory results in only one susceptibility tensor covering all the electric, magnetic and chiral polarizations, and the book provides its quantum mechanical expression in terms of the transition energies of matter and the lower moments of corresponding current density matrix elements. The conventional theory in terms of epsilon and mu is recovered in the absence of chirality under the condition that magnetic susceptibility is defined with respect to not H, but to B. This new edition includes discussions supporting the basis of the present electromagnetic response theory in a weakly relativistic regime, showing the gauge invariance of many-body Schroedinger equation with explicit Coulomb potential, the relationship between this theory and the emergent electromagnetism, and the choice of appropriate forms of single susceptibility theory and chiral constitutive equations.

This book contains 157 problems in classical electromagnetism, most of them new and original compared to those found in other textbooks. Each problem is presented with a title in order to highlight its inspiration in different areas of physics or technology, so that the book is also a survey of historical discoveries and applications of classical electromagnetism. The solutions are complete and include detailed discussions, which take into account typical questions and mistakes by the students. Without unnecessary mathematical complexity, the problems and related discussions introduce the student to advanced concepts such as unipolar and homopolar motors, magnetic monopoles, radiation pressure, angular momentum of light, bulk and surface plasmons, radiation friction, as well as to tricky concepts and ostensible ambiguities or paradoxes related to the classical theory of the electromagnetic field. With this approach the book is both a teaching tool for undergraduates in physics, mathematics and electric engineering, and a reference for students wishing to work in optics, material science, electronics, plasma physics.

Focusing on the interface between mathematics and physics, this book offers an introduction to the physics, the mathematics, and the numerical simulation of nonlinear systems in optics and atomic physics. The text covers a wide spectrum of current research on the subject, which is an extremely active field in physics and mathematical physics, with a very broad range of implications, both for fundamental science and technological applications: light propagation in microstructured optical fibers, Bose-Einstein condensates, disordered systems, and the newly emerging field of nonlinear quantum mechanics. Accessible to PhD students, this book will also be of interest to post-doctoral researchers and seasoned academics.

This book focusses on the state of the art of Monte Carlo methods in radiation physics and particle transport simulation and applications, the latter involving in particular, the use and development of electron--gamma, neutron--gamma and hadronic codes. Besides the basic theory and the methods employed, special attention is paid to algorithm development for modeling, and the analysis of experiments and measurements in a variety of fields ranging from particle to medical physics.

HISTORICAL PRELUDE Ettore Majorana's fame solidly rests on testimonies like the following, from the evocative pen of Giuseppe Cocconi. At the request of Edoardo Amaldi, he wrote from CERN (July 18, 1965):'In January 1938, after having just graduated, I was invited, essen­ tially by you, to come to the Institute of Physics at the University in Rome for six months as a teaching assistant, and once I was there I would have the good fortune of joining Fermi, Bernardini (who had been given a chair at Camerino a few months earlier) and Ageno (he, too, a new graduate), in the research of the products of disintegration of /-L'mesons'(at that time called mesotrons or yukons), which are produced by cosmic rays [... ]'It was actually while I was staying with Fermi in the small laboratory on the second floor, absorbed in our work, with Fermi working with a piece of Wilson's chamber (which would help to reveal mesons at the end of their range) on a lathe and me constructing a jalopy for the illumination of the chamber, using the flash produced by the explosion of an aluminum ribbon short circuited on a battery, that Ettore Majorana came in search of Fermi. I was introduced to him and we exchanged few words. A dark face. And that was it.

Proceedings of the 14th Winter Workshop held in Snowbird, Utah, January 31-February 7, 1998

This edition combines the earlier two volumes on Quantum Mechanics of Atoms and Molecules and on Quantum Mechanics of Large Systems, thus including in a single volume the material for a two-semester course on quantum physics. Since this volume is already quite heavy, I could not include many new results which show how lively the subject is. I just want to mention that inequality (IV:4. 1. l. 1) has been sharpened by T. Weidl by a factor 2][ and the difficult problem 1 of (III:4. 6) has been solved by A. Martin. I have to thank N. Ilieva for the devotion in preparing this new edition. Vienna, November 2001 Walter Thirring Preface to the Second Edition: Quantum Mechanics of Atoms and Molecules Ever since the first edition of this volume appeared in 1980 quantum statistical mechanics has florished. Innumerable results in many areas have been obtained and it would require a series of volumes to do justice to all of them. On the other hand the first edition was already rather crowded with many details so it would not be overburdened any more. Thus I added only one chapter on quantum ergodic theory where one can get the main notions across without too much pain. Nevertheless many subjects treated in the book had splendidely developed ever since and the only way out I could see is to add some recent references which the interested reader can consult.

It may tum out that, like certain other phenomena studied by sociologists, bouts of interest in the foundations of quantum mechanics tend to come in 60-year cycles. It is hardly surprising that in the first decade or so of the subject the conceptual puzzles generated by this strange new way of looking at the world should have generated profound interest, not just among professional physicists themselves but also among philosophers and informed laymen; but this intense interest was followed by a fallow period in the forties and fifties when the physics establishment by and large took the view that the only puzzles left were the product either of incompetent application of the formalism or of bad philosophy, and only a few brave individualists like the late David Bohm dared to suggest that maybe there really was something there after all to worry about. As Bell and Nauenberg, surveying the scene in 1966, put it:'The typical physicist feels that [these questions 1 have long ago been answered, and that he will fully understand how if ever he can spare twenty minutes to think about it.'But gradually, through the sixties and seventies, curiosity did revive, and the last ten years or so have seen a level of interest in foundational questions, and an involvement in them by some of the leading figures of contemporary physics, which is probably unparalleled since the earliest days.

Approach your problems from the It isn't that they can't see the end and begin with the answers. solution. It is that they can't Then one day, perhaps you will see the problem. find the final question. G.K. Chesterton. The Scandal of'The Hermit Clad in Crane Father Brown'The Point of a Pin'. Feathers'in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono­ graphs and textbooks on increasingly topics. However, the'tree'of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro­ gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electric engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as'complete integrable systems','chaos, synergetics and large-scale order', which are almost impossible to fit into the existing classifica­ tion schemes. The draw upon widely different sections of mathematics.

This volume records the proceedings of a Forum on The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State held at the Coseners'House, Abingdon-on-Thames, Oxon. over the period 31st May - 2nd June, 2002. The forum consisted of 26 oral and poster presentations followed by a discussion structure around questions and comments submitted by the participants (and others who had expressed an interest) in advance of the meeting. Quantum mechanics provides a theoretical foundation for our under­ standing of the structure and properties of atoms, molecules and the solid state in terms their component particles, electrons and nuclei. (Rel­ ativistic quantum mechanics is required for molecular systems contain­ ing heavy atoms.) However, the solution of the equations of quantum mechanics yields a function, a wave function, which depends on the co­ ordinates, both space and spin, of all of the particles in the system. This functions contains much more information than is required to yield the energy or other property.

This book addresses hybrid simulation of plasmas; it is aimed at developing insight into the essence of plasma behavior. Major current applications are to astrophysical and space plasmas. Some applications are connected with active experiments in space. However, hybrid simulations are also being used to gain an understanding of basic plasma phenomena such as particle acceleration by shocks, magnetic field reconnect ion in neutral current sheets, generation of waves by beams, mass loading of the supersonic flow by heavy pickup ions and the dynamics of tangential discontinuities. Such simulations may be very important not only for the study of the astrophysical plasmas, but also for the study of the magnetically and inertially contained fusion plasmas, and other laboratory plasma devices. Plasma is the fourth state of matter, consisting of electrons, ions and 4 neutral atoms, usually at temperatures above 10 K. The stars and sun are plasmas; the local interstellar medium, the solar wind, magnetospheres and ionospheres of planets and comets, Van-Allen belts, etc., are all plasmas. Indeed, much of the known matter in the universe is plasma.

This book gives a detailed overview of the theory of electromagnetic wave scattering on single, homogeneous, but nonspherical particles. Beside the systematically developed Green's function formalism of the first edition this second and enlarged edition contains additional material regarding group theoretical considerations for nonspherical particles with boundary symmetries, an iterative T-matrix scheme for approximate solutions, and two additional but basic applications. Moreover, to demonstrate the advantages of the group theoretical approach and the iterative solution technique, the restriction to axisymmetric scatterers of the first edition was abandoned.

Volume 21 provides the basis of the MHD theory in two extended reviews. The first review deals with high-temperature plasma equilibrium and stability in conventional stellarators (the steady state three-dimensional magnetic confinement systems). The second review considers the processes in the stationary plasma thrusters (SPT) created by one of the authors, A.I Morozov. In spite of the three-dimensional nature of stellarators, the author of the review, V.D. Pustovitov, has been able to give a concise presentation of basic ideas and results of the rather complicated theory of stellarators, both for specialists and for students in this field. The results of experimental and theoretical investigations of a new type of discharge device, SPT, are presented in the second review. Plasma thrusters generate quasi-neutral multi-ampere streams of ions with particle energies of 50 - 1000eV. They are most widely known as electric propulsion thrusters for spacecraft, and have been mounted onboard more than 50 Russian satellites. In addition, the SPTs are now used in technological systems for processing the surface layers of various products.

Proceedings of the International Symposium on Supercomputing held in Tokyo, Japan, September 1-3, 1997

Because magnetically confined plasmas are generally not found in a state of thermodynamic equilibrium, they have been studied extensively with methods of applied kinetic theory. In closed magnetic field line confinement devices such as the tokamak, non-Maxwellian distortions usually occur as a result of auxiliary heating and transport. In magnetic mirror configurations even the intended steady state plasma is far from local thermodynamic equilibrium because of losses along open magnetic field lines. In both of these major fusion devices, kinetic models based on the Boltzmann equation with Fokker-Planck collision terms have been successful in representing plasma behavior. The heating of plasmas by energetic neutral beams or microwaves, the production and thermalization of a-particles in thermonuclear reactor plasmas, the study of runaway electrons in tokamaks, and the performance of two-energy compo­ nent fusion reactors are some examples of processes in which the solution of kinetic equations is appropriate and, moreover, generally necessary for an understanding of the plasma dynamics. Ultimately, the problem is to solve a nonlinear partial differential equation for the distribution function of each charged plasma species in terms of six phase space variables and time. The dimensionality of the problem may be reduced through imposing certain symmetry conditions. For example, fewer spatial dimensions are needed if either the magnetic field is taken to be uniform or the magnetic field inhomogeneity enters principally through its variation along the direction of the field.

The emergence and spectacularly rapid evolution of the field of atomic and molecular clusters are among the most exciting developments in the recent history of natural sciences. The field of clusters expands into the traditional disciplines of physics, chemistry, materials science, and biology, yet in many respects it forms a cognition area of its own. This book presents a cross section of theoretical approaches and their applications in studies of different cluster systems. The contributions are written by experts in the respective areas. The systems discussed range from weakly (van der Waals) bonded, through hydrogen- and covalently bonded, to semiconductor and metallic clusters. The theoretical approaches involve high-level electronic structure computations, more approximate electronic structure treatments, use of semiempirical potentials, dynamical and statistical analyses, and illustrate the utility of both classical and quantum mechanical concepts.

Flux Coordinates and Magnetic Field Structure gives a systematic and rigorous presentation of the mathematical framework and principles underlying the description of magnetically confined fusion plasmas. After a brief treatment of vector algebra in curvilinear coordinate systems the book introduces concepts such as flux surfaces, rotational transforms, and magnetic differential equations. The various specific types of coordinate system are dealt with in detail. Researchers and advanced students in plasma physics, electromagnetics, and mathematical physics will greatly benefit from this useful guide and reference book.

The search for examples of proton radioactivity has resulted in the discovery of a large number of proton emitters in the region 50 < Z < 84 [1]. Many of these proton emitters and their daughters are also a-emitters, and in some cases the a-decay chain from the daughter terminates on a nuclide closer to stability whose mass excess is known. This opens up the possibility of using a-and proton-decay Q-values to determine the mass excesses of a large group of nuclei connected by particle decay. The Q-values are derived from the measured kinetic energies of the emitted protons or a-particles. Where the decay chains are not connected to nuclei with known mass excesses, proton separation energies can be measured in some cases and derived in others. For the a-decay ofthe parent nucleus (Z, A) to the daughter (Z - 2, A - 4), the energy and momentum relations used to convert between Q-value, mass (M) and mass excess (ME) are: M(4He)E', (1) M(Z - 2, A - 4)Erecoil, (2) Q', E', + Erecoi\, ME(Z, A) Q', + ME(Z - 2, A - 4) + ME(4He). (3) In practice, one uses M(4He) ~ 4 and M(Z - 2, A - 4) (A - 4), so that Equation (3) becomes ME(Z, A) = E', (_A_) + ME(Z - 2, A - 4) + ME(4He). (4) A -4 Similarly, for protons, we have ME(Z, A) = Ep(_A_) +ME(Z - 1, A-I) +ME(lH).

Density Functional Theory is a rapidly developing branch of many-particle physics that has found applications in atomic, molecular, solid-state and nuclear physics. This book describes the conceptual framework of density functional theory and discusses in detail the derivation of explicit functionals from first principles as well as their application to Coulomb systems. Both non-relativistic and relativistic systems are treated. The connection of density functional theory with other many-body methods is highlighted. The presentation is self-contained; the book is, thus, well suited for a graduate course on density functional theory.

Quantum theory is one of the most fascinating and successful constructs in the intellectual history of mankind. Nonetheless, the theory has very shaky philosophical foundations. This book contains thoughtful discussions by eminent researchers of a spate of experimental techniques newly developed to test some of the stranger predictions of quantum physics. The advances considered include recent experiments in quantum optics, electron and ion interferometry, photon down conversion in nonlinear crystals, single trapped ions interacting with laser beams, atom-field coupling in micromaser cavities, quantum computation, quantum cryptography, decoherence and macroscopic quantum effects, the quantum state diffusion model, quantum gravity, the quantum mechanics of cosmology and quantum non-locality along with the continuing debate surrounding the interpretation of quantum mechanics. Audience: The book is intended for physicists, philosophers of science, mathematicians, graduate students and those interested in the foundations of quantum theory.

Nuclei in their ground states behave as quantum fluids, Fermi liquids. When the density, or the temperature of that fluid increases, various phase transitions may occur. Thus, for moderate excitation energies, of the order of a few MeV per nucleon, nuclear matter behaves as an ordinary fluid with gaseous and liquid phases, and a coexistence region below a critical temperature. For higher excitation energies, of the order of a few Ge V per nucleon, the composition of nuclear matter changes, nucleons being gradually turned into baryonic resonances of various kinds. Finally, when 3 the energy density exceeds some few GeV /fm, nuclear matter turns into a gas of weakly interacting quarks and gluons. This new phase of matter has been called the quark-gluon plasma, and its existence is a prediction of Quantum Chromodynamics. Collisions of heavy ions produce nuclear matter with various degrees of excitation. In fact, by selecting the impact parameter and the bombarding energy, one can produce nuclear matter with specified baryonic density and excitation energy. Several major experimental programs are under way (for instance at GANIL, with the detector INDRA, at GSI with the detector ALADIN, at the CERN-SPS, at the AGS of Brookhaven, etc.), or are in preparation (RRIC, LHC, etc.). The goal of these experiments is to get evidence for the different phases of nuclear matter predicted by the theory, and to study their properties.

Proceedings of an International Conference on Current Developments in Atomic, Molecular, and Chemical Physics with Applications, held March 20-22, 2002, in Delhi, India. The 38 chapters cover a broad range of research activities categorized into four sub-topics, namely: • Processes in Laser Fields, • Chemical Physics, • Collision Processes, • Atomic Structure and Applications.

This book is devoted to mathematical modeling of tokamak plasma. Since the appearance in 1982 of the first edition (in Russian), a considerable amount of experimental and theoretical material on tokamak research has been accumu­ lated. The new-generation devices, viz., TFTR, JET and JT-60 were put into operation. The first experiments on these units have confirmed the correctness of the basic physical concepts underlying their construction. Experiments on plasma heating with the help of neutral beams and high-frequency (HF) waves on previous generation devices made it possible to obtain high-P plasmas. The number of'medium-size'tokamaks in operation has increased. New experi­ mental results and advances in the theory have led to more complicated and perfected models of high-temperature plasma. Rapid progress in computer hardware and software has played an important role in the further development of mathematical modeling. While preparing the English edition of the book, we have revised the text considerably. Several new models which have undergone significant advance­ ment in recent years are described. A section devoted to models of RF (radio frequency) current drive has been added to Chap. 2. The reduced magneto­ hydrodynamic (MHD) equations for high-P plasma are now considered in detail in Chap. 3. Chapter 4 contains the latest results on anomalous thermal conductivity, diffusion coefficient and pinching. Two new sections are added to Chap. 5.

Nuclear many-body theory provides the foundation for understanding and exploiting the new generation of experimental probes of nuclear structure that are now becoming available. The twentieth volume of Advances in Nuclear Physics is thus devoted to two major theoretical chapters addressing two fundamental issues: understanding single-particle properties in nuclei and the consistent formulation of a relativistic theory appropriate for hadronic physics. The long-standing problem of understanding single-particle behavior in a strongly interacting nuclear system takes on new urgency and sig­ nificance in the face of detailed measurements of the nuclear spectral function in (e, e'p) experiments. In the first chapter, Mahaux and Sartor confront head-on the ambiguities in defining single-particle properties and the limitations in calculating them microscopically. This thoughtful chapter provides a thorough, pedagogical review of the relevant aspects of many­ body theory and of previous treatments in the nuclear physics literature. It also presents the author's own vision of how to properly formulate and understand single-particle behavior based on the self-energy, or mass operator. Their approach provides a powerful, unified description of the nuclear mean field that covers negative as well as positive energies and consistently fills in that information that cannot yet be calculated reliably microscopically by a theoretically motivated phenomenology. Particular emphasis is placed upon experiment, both in the exhaustive comparisons with experimental data and in the detailed discussion of the relations of each of the theoretical quantities defined in the chapter to physical observables.

The quest for many-body techniques and approximations to describe the essential physics of strongly interacting systems with many degrees of freedom is one of the central themes of contemporary nuclear physics. The three articles in this volume describe advances in this quest in three dif­ ferent areas of nuclear many-body physics: multi quark degrees of freedom in nucleon-nucleon interactions and light nuclei, multinucleon clusters in many-nucleon wave functions and reactions, and the nuclear-shell model. In each case the common issues arise of identifying the relevant degrees of freedom, truncating those that are inessential, formulating tractable approximations, and judiciously invoking phenomenology when it is not possible to proceed from first principles. Indeed, the parallels between the different applications are often striking, as in the case of the similarities in the treatment of clusters of quarks in nucleon-nucleon interactions and clusters of nucleons in nuclear reactions, and the central role of the resonating group approximation in treating both. Despite two decades of effort since the experimental discovery of quarks in nucleons, we are still far from a derivation of nucleon structure and nucleon-nucleon interactions directly from quantum chromodynamics.

This IMA Volume in Mathematics and its Applications MULTIPARTICLE QUANTUM SCATTERING WITH APPLICATIONS TO NUCLEAR, ATOMIC AND MOLECULAR PHYSICS is based on the proceedings of a workshop with the same title, which was an integral part of the 1994-1995 IMA program on'Waves and Scattering.'We would like to thank Donald G. Truhlar and Barry Simon for their ex­ cellent work as organizers of this meeting and as editors of the proceedings. We also take this opportunity to thank the National Science Foundation (NSF), the Army Research Office (ARO), and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE The workshop on Multiparticle Quantum Scattering with Applications to Nuclear, Atomic, and Molecular Physics was held June 12-16, 1995 at the Institute for Mathematics and Its Applications in the University of Min­ nesota Twin Cities campus as part of the 1994-95 Program on Waves and Scattering. There were about seventy participants including the plenary lecturers whose contributions are included in this volume. The workshop was preceded by a two-day tutorial featuring lectures by Donald J. Kouri and Gian Michele Graf, and we are pleased that both Professors Graf and Kouri were able to write up their tutorials as opening chapters of this volume.

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.

A comprehensive survey of recent theoretical and experimental progress in the area of electron-photon interaction and dense media. A state-of-the-art discussion of radiation production, with descriptions of new ideas and technologies that enhance the production of X-rays in the form of channelling, transition and parametric X-ray production. Progress in electron beam physics to produce sub-picosecond electron bunches from low-energy linear accelerators make it possible to produce coherent, high brightness, submillimeter radiation and sub-picosecond X-ray pulses. Micro-undulators in the form of bent crystalline structures hold great promise as future X-ray sources.

Reviews of Plasma Physics, Volume 23, presents two high quality reviews from the cutting-edge of Russian plasma physics research:'Plasma Models of Atom and Radiative-Collisional Processes', by V.A. Astapenko, L.A. Bureyeva, V.S. Lisitsa, is devoted to a unified description of the atomic core polarization effects in the free-free, free-bound and bound-bound transitions of the charged particles in the field of multielectron atom.'Asymptotic Theory of Charge Exchange And Mobility Processes for Atomic Ions'by B.M. Smirnov reviews the process of resonant charge exchange, and also the transport processes (mobility and diffusion coefficients) for ions in parent gases which are determined by resonant electron transfer.

The recent developement of high power lasers, delivering femtosecond pulses of 20 2 intensities up to 10 W/cm, has led to the discovery of new phenomena in laser interactions with matter. At these enormous laser intensities, atoms, and molecules are exposed to extreme conditions and new phenomena occur, such as the very rapid multi photon ionization of atomic systems, the emission by these systems of very high order harmonics of the exciting laser light, the Coulomb explosion of molecules, and the acceleration of electrons close to the velocity of light. These phenomena generate new behaviour of bulk matter in intense laser fields, with great potential for wide ranging applications which include the study of ultra-fast processes, the development of high-frequency lasers, and the investigation of the properties of plasmas and condensed matter under extreme conditions of temperature and pressure. In particular, the concept of the'fast ignitor'approach to inertial confinement fusion (ICF) has been proposed, which is based on the separation of the compression and the ignition phases in laser-driven ICF. The aim of this course on'Atom, Solids and Plasmas in Super-Intense Laser fields'was to bring together senior researchers and students in atomic and molecular physics, laser physics, condensed matter and plasma physics, in order to review recent developments in high-intensity laser-matter interactions. The course was held at the Ettore Majorana International Centre for Scientific Culture in Erice from July 8 to July 14,2000.

'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.

New developments for hydrodynamical dynamo theory have been spurred by recent evidence of self-sustained dynamo activity in laboratory experiments with liquid metals.The emphasis in the present volume is on the introduction of powerful mathematical techniques required to tackle modern multiscale analysis of continous systems and there application to a number of realistic model geometries of increasing complexity. This introductory and self-contained research monograph summarizes the theoretical state-of-the-art to which the author has made pioneering contributions.

This thesis addresses optical binding - a new area of interest within the field of optical micromanipulation. It presents, for the first time, a rigorous numerical simulation of some of the key results, along with new experimental findings and also physical interpretations of the results. In an optical trap particles are attracted close to areas of high optical intensities and intensity gradients. So, for example, if two lasers are pointed towards each other (a counter propagating trap) then a single particle is trapped in the centre of the two beams – the system is analogous to a particle being held by two springs in a potential well. If one increases the number of particles in the trap then naively one would expect all the particles to collect in the centre of the well. However, the effect of optical binding means that the presence of one particle affects the distribution of light experienced by another particle, resulting in extremely complex interactions that can lead to unusual 1D and 2D structures to form within the trap. Optical binding is not only of theoretical interest but also has applications in micromanipulation and assembly.

But all the clocks in the city Began to whirr and chime:'O let not Time deceive you, You cannot conquer Time. W. H. Auden It is hard to think of a subject as rich, complex, and important as time. From the practical point of view it governs and organizes our lives (most of us are after all attached to a wrist watch) or it helps us to wonderfully?nd our way in unknown territory with the global positioning system (GPS). More generally it constitutes the heartbeat of modern technology. Time is the most precisely measured quantity, so the second de?nes the meter or the volt and yet, nobody knows for sure what it is, puzzling philosophers, artists, priests, and scientists for centuries as one of the enduring enigmas of all cultures. Indeed time is full of contrasts: taken for granted in daily life, it requires sophisticated experimental and theoretical treatments to be accurately “produced. ” We are trapped in its web, and it actually kills us all, but it also constitutes the stuff we need to progress and realize our objectives. There is nothing more boring and monotonous than the tick-tock of a clock, but how many fascinating challenges have physicists met to realize that monotony: Quite a number of Nobel Prize winners have been directly motivated by them or have contributed 1 signi?cantly to time measurement.

This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries. Differential and integro-differential equations, especially nonlinear, present the most effective way for describing complex processes. Therefore, methods to obtain exact solutions of differential equations play an important role in physics, applied mathematics and mechanics. This book provides an easy to follow, but comprehensive, description of the application of group analysis to integro-differential equations. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. It introduces new applications and extensions of the group analysis method. The authors have designed a flexible text for postgraduate courses spanning a variety of topics.

Published under the auspices of the Royal Astronomical Society, this volume contains a set of extensive school tested lectures, with the aim to give a coherent and thorough background knowledge of the subject and to introduce the latest developments in N-body computational astrophysics. The topics cover a wide range from the classical few-body problem with discussions of resonance, chaos and stability to realistic modelling of star clusters as well as descriptions of codes, algorithms and special hardware for N-body simulations. This collection of topics, related to the gravitational N-body problem, will prove useful to both students and researchers in years to come.1) Published under the auspices of the Royal Astronomical Society.

This book is a tribute to the life and work of J Q Chen. The contributions of Chen to nuclear and molecular physics are discussed vis-à-vis present developments in these fields. Among other subjects, the present status of microscopic theories of the interacting boson model in nuclear physics and the theory of symmetry adaptation of molecular vibrations in molecular physics are reviewed. The latter theory is particularly useful for large molecular species such as fullerenes, where icosahedral symmetry plays a fundamental role.