Bøger i NATO Science Series B serien

This volume contains the lectures and invited seminars pre­ sented at the NATO Advanced Study Institute on NON-EQUILIBRIUM COOPERATIVE PHENOMENA IN PHYSICS AND RELATED FIELDS that was held at EL ESCORIAL (MADRID), SPAIN, on August 1-11, 1983. Most nonlinear problems in dissipative systems, i . e . , most mathematical models in SYNERGETICS are highly trans disciplinary in practice and the list of lecturers and participants at the ASI reflects this di versi ty both in background and interest. The presentation of the material fell into two main categories: tutopia~ Zectures on some basic ideas and methods, both experimental and theoretical, intended to lay a common base for all participants, and a series of more specific lectures and seminars, serving the purpose of exemplying selected but typical applications in their current state of development. Topics were chosen for their basic interest as well as for their potential for applications (laser, hydrodynamics, liquid crystals, EHD, combustion, thermoelasticity, etc. ). We had more seminars and some of the oral presentations were supported or complemented with 16 mm films and on occasion with experimental demonstrations including a special seminar, a social one on broken symmetries in Art and Music. There is here no record of these non-standard acti vi ties. We had, indeed, quite a heavy load for which I was fully responsible. However, the reader and, above all, the participants at the ASI ought to be aware of the fact that in Spain, with.

This book comprises the Proceedings of a NATO Advanced Study Institute on Mu1ticritica1 Phenomena held in Geilo, Norway, between 10-21 April 1983. This school was the seventh to be held in Gei10, on various aspects of phase transitions. In spite of its apparently restrictive title the school was planned as a forum for the discus­ sion of phase transitions and instabilities in systems, with competing interactions and competing order parameters. Thus, in addition to the canonical multicritical points, subjects were diverse as critical phenomena in random magnetic systems and routes to chaos were discussed. The subject matter of the school is naturally divided into a series of categories which to some extent, reflect the historical development of interest in competing phenomena at phase transitions. Multicritical points in equilibrium systems, defined phenomenolo­ gically as points of sudden change of behaviour on an otherwise smooth phase boundary, were the first topics of the school. The theo­ retical consensus which has emerged during the past decade, largely as a result of calculations with the renormalisation group, was reviewed in some detail. The results presented, however, apply only to pure systems (in which dirt and other manifestations of reality are irrelevant) in that small realm close to the phase transition knoYln as "asymtopia.

Each summer, the Theoretical Physics Division of the Canadian Association of Physicists organizes a summer institute of two weeks duration on a current topic in theoretical physics. This volume contains the lectures from the Pacific Summer Institute held at Pearson College on Vancouver Island, B. C. (Canada) from August 23 to September 3, 1982. The Institute was titled "Progress in Nuclear Dynamics: Short-Distance Behavior in the Nucleus". The primary source of funds for the Institute came from NATO through its Advanced Study Institute programme. Significant finan­ cial support is also gratefully acknowledged from TRIUMF, Simon Fraser University, Natural Sciences and Engineering Research Council of Canada, and Atomic Energy of Canada Ltd. The topic of the school was the role of the substructure of hadrons--quarks and gluons--in nuclear physics. This includes not only the effects which may be observed in specific nuclear states, such as form factors at large momentum transfer, or the presence of hidden color components in the ground states of few nucleon systems, but also effects which may be observed in the nuclear matter contin­ uum: the phase transition from normal nuclear matter to a plasma of quarks and gluons. The current status of the long distance phenom­ enology of the nucleus--the interacting boson approximation and the role of n's and ~'s in nuclear structure, is also reviewed.

In 1269 Petrus Peregrinus observed lines of force around a lodestone and noted that they were concentrated at two points which he designated as the north and south poles of the magnet. Subsequent observation has confirmed that all magnetic objects have paired regions of' opposite polarity, that is, all magnets are dipoles. It is easy to conceive of an isolated pole, which J.J. Thomson did in 1904 when he set his famous problem of the motion of an electron in the field of a magnetic charge. In 1931 P.A.M. Dirac solved this problem quantum mechanically and showed that the existence of a single magnet pole anywhere in the universe could explain the mystery of charge quantization. By late 1981, theoretical interest in monopoles had reached the point where a meeting was organized at the International Centre for Theoretical Physics in Trieste. Many mathematical properties of monopoles were discussed at length but there was only a solitary account describing experiments. This imbalance did not so much reflect the meeting's venue as it indicated the relative theoretical and experimental effort at that point.

The second Advanced Study Institute (ASI) on Techniques and Concepts of High Energy Physics was held at the Roaring Brook Resort at Lake George, New York. As in the case of the first ASI, our aim was to bring together a small group of promising young ex­ perimenters and several outstanding senior scholars in high energy physics in order to learn about the latest trends in the field and develop stronger contacts among scientists from different countries and different backgrounds. The setting at Roaring Brook was particularly congenial and the staff, under the direction of George Green, was both friendly and efficient. The ASI was supported mainly through funds provided by the Scientific Affairs Division of NATO. It was cosponsored by the U. S. Department of Energy, Fermilab, the National Science Founda­ tion and the University of Rochester. A special grant from the Oliver S. and Jennie R. Donaldson Charitable Trust provided a valuable degree of flexibility for supporting worthy students. The scientific program of this ASI was, once again, designed primarily for advanced graduate students and recent Ph.D recipients in experimental particle physics. I believe, however, that the contents of the present volume will prove useful to an even wider audience of physicists.

This book presents an ac count of the NATO Advanced Study Institute on "Collective Excitations in Solids," held in Erice, Italy, from June 15 to June 29, 1981. This meeting was organized by the International School of Atomic and Molecular Spectroscopy of the "Ettore Majorana" Centre for Scientific Culture. The objective of the Institute was to formulate a unified and coherent treatment of various collective excitation processes by drawing on the current advances in various branches of the physics of the solid state. A total of 74 participants came from 54 laboratories and 20 nations (Australia, Belgium, Burma, Canada, China, France, F. R. Germany, Greece, Israel, Italy, Mexico, The Netherlands, Pakistan, Poland, Portugal, Romania, Switzerland, Turkey, The Uni ted Kingdom, and The United States). The secretaries of the course were: Joseph Danko for the scientific aspects and Nino La Francesca for the administrative aspects of the meeting. Fourty-four lectures divided in eleven series were given. Nine "long" seminars and eight "short" seminars were also presented. In addition, two round-table discussions were held.

One of the goals of mathematical physics is to provide a rigorous derivation of the properties of macroscopic matter starting from Schrodinger's equation. Although at the present time this objective is far from being realized, there has been striking recent progress, and the fourth "Ettore Majorana" International School of Mathematical Physics held at Erice, 1-15 June 1980 with the title Rigorous Atomic and Mqlecular Physics focussed on some of the recent advances. The first of these is the geometric method in the theory of scattering. Quantum mechanical scattering theory is an old and highly cultivated subject, but, until recently, many of its fundamental developments were technically very complicated and conceptually rather obscure. For example, one of the basic properties of a system of N particles moving under the influence of appropriately restricted short-range plus Coulomb forces is asymptotic completeness: the space of states is spanned by the bound states and scattering states. However, the proof of asymp­ totic. completeness for N bodies was achieved only with physically unsatisfactory restrictions on the nature of the interaction and even for N = 2 required an involved argument rather more subtle than the physical circumstances seemed to warrant. The reader will find in the present volume a very simple and physical proof of asymptotic completeness for N = 2 as well as an outline of the geometrical ideas which are currently being used to attack the problem for N > 2. (See the lectures of Enss.

The importance of phonons has long been recognized by research­ ers in nonequilibrium superconductivity. Similarly, experimentalists studying phonons at low temperatures have relied heavily on supercon­ ductors as sources and detectors. To a large extent this symbiotic relationship has developed with a general mutual awareness; however, to our knowledge these subjects have never been treated together in conferences or study institutes. It was with the hope of further contributing to the awareness and communication between workers in these areas that this NATO Advanced Study Institute (ASI) has been conceived. A second, but equally important, reason for holding this ASI is to fill a void by providing the first general textbook in this important area of physics. Therefore, there was an emphasis on the tutorial nature of the lectures and written contributions to this textbook. It should not go unnoticed that the experimental and theoretical concepts covered in this textbook are of paramount importance to the various applications of superconductors. Almost by definition, the use of a superconductor implies a nonequilibrium state! For example, phonon conduction to the helium bath is important in devices ranging from microscopic Josephson junctions to large scale magnets and transmission lines. Knowledge of the more fundamental nonequilibrium effects can aid in our understanding of devices as well as provide the potential for entirely new applications.

For the Sixth Course of the International School of Cosmology and Gravitation of the "Ettore Maj orana" Centre for Scientific Cul­ ture we choose as the principal topics torsion and supergravity, because in our opinion it is one of the principal tasks of today's theoretical physics to attempt to link together the theory of ele­ mentary particles and general relativity. Our aim was to delineate the present status of the principal efforts directed toward this end, and to explore possible directions of work in the near future. Efforts to incorporate spin as a dynamic variable into the foundations of the theory of gravitation were poineered by E. Cartan, whose contributions to this problem go back half a century. Accord­ ing to A. Trautman this so-called Einstein-Cartan theory is the sim­ plest and most natural modification of Einstein's 1916 theory. F. Hehl has contributed a very detailed and comprehensive analysis of this topic, original view of non-Riemannian space-time. Characteristic of Einstein-Cartan theories is the enrichment of Riemannian geometry by torsion, the non-symmetric part of the otherwise metric-compatible affine connection. Torsion has a impact on the theory of elementary particles. According to V. de Sabbata, weak interactions can be based on the Einstein-Cartan geometry, in that the Lagrangian describing weak interactions and torsion inter-­ action possess analogous structures, leading to a unification of weak and gravitational forces.

The Advanced Study Institute on Field Theoretical Methods in Particle Physics was held at the Universitat Kaiserslautern in Kaiserslautern, Germany, from August 13 to August 24, 1979. Twenty invited lectures and seminar-speakers and 100 other participants attended this Institute. The contributions of most of the lecturers and seminar-speakers are contained in this volume. The revival of field theory in elementary particle physics that started about ten years ago has influenced all branches of elementary particle physics from fundamental research to pure phenomenology. The selection of field theoretical methods in part­ icle physics appropriate for the Institute is therefore the first task for the organizers. We decided to have constructive problems of gauge field theories and solvable models as two major areas to be covered during the Institute. If one considers the concepts and terminology currently used by pure field theorists, one notices that many of them were introduced and discussed first by pheno­ menologists in comparing quite elementary models directly with experimental data. For this reason, it seemed worthwhile to re­ serve considerable time to phenomenological field theory. The Institute was sponsored by the North Atlantic Treaty Organization whose funds made the Institute possible. It was co­ sponsored by the Bundes-Ministerium fur Forschung und Technologie in Bonn and the Landes-Ministerium fUr Kultus in Mainz. The City of Kaiserslautern made the Theodor Zink Museum avail­ able for a reception. Thanks are due in particular to its director, Dr. Dunkel.

The area of high field transport in semiconductors has been of interest since the early studies of dielectric breakdown in various materials. It really emerged as a sub-discipline of semiconductor physics in the early 1960's, following the discovery of substantial deviations from Ohm's law at high electric fields. Since that time, it has become a major area of importance in solid state electronics as semiconductor devices have operated at higher frequencies and higher powers. It has become apparent since the Modena Conference on Hot Electrons in 1973, that the area of hot electrons has ex­ tended weIl beyond the concept of semi-classical electrons (or holes) in homogeneous semiconductor materials. This was exemplified by the broad range of papers presented at the International Conference on Hot Electrons in Semiconductors, held in Denton, Texas, in 1977. Hot electron physics has progressed from a limited phenomeno­ logical science to a full-fledged experimental and precision theo­ retical science. The conceptual base and subsequent applications have been widened and underpinned by the development of ab initio nonlinear quantum transport theory which complements and identifies the limitations of the traditional semi-classical Boltzmann-Bloch picture. Such diverse areas as large polarons, pico-second laser excitation, quantum magneto-transport, sub-three dimensional systems, and of course device dynamics all have been shown to be strongly interactive with more classical hot electron pictures.

This volume contains the proceedings of a NATO Advanced Study Institute devoted to the study of dynamical correlation functions of the form (I) J~e-lwt 6ft T- is an equilibrium average. In equation (1) it is useful to regard the product AB as the product of two operators in cases in which A and B refer to different spatial points in a condensed matter sys­ tem and/or in which A and B behave dynamically in a quasiharmonic way. In the second case, one has a two quasiparticle correlation function and CAB;AB(w) gives information about quasiparticle inter­ actions. Condensed matter physics has increasingly turned its attention to correlation functions of this type during the last 15 years, partly because the two point and/or one-particle correlation functions have by now been very thoroughly studied in many cases. The study of four point and/or two quasiparticle correlations has proceeded somewhat independently in several diverse fields of condensed matter physics and it was one purpose of the institute to bring experts from these different fields together to describe the current state of their art to each other and to advanced students.

This Advanced Study Institute on the topic of SOLID STATE MICROBATTERIES is the third and final institute on the general theme of a field of study now termed "e;SOLID STATE IONICS"e;. The institute was held in Erice, Sicily, Italy, 3 - 15 July 1988. The objective was to assemble in one location individuals from industry and academia expert in the fields of microelectronics and solid state ionics to determine the feasibility of merging a solid state microbattery with microelectronic memory. Solid electrolytes are in principle amenable to vapor deposition, RF or DC sputtering, and other techniques used to fabricate microelectronic components. A solid state microbattery 1 1 mated on the same chip carrier as the chip can provide on board memory backup power. A solid state microbattery assembled from properly selected anode/solid electrolyte/cathode materials could have environmental endurance properties equal or superior to semiconductor memory chips. Lectures covering microelectronics, present state-of-art solid state batteries, new solid electrolyte cathode materials, theoretical and practical techniques for fabrication of new solid electrolytes, and analytical techniques for study of solid electrolytes were covered. Several areas where effort is required for further understanding of materials in pure form and their interactions with other materials at interfacial contact points were identified. Cathode materials for solid state batteries is one particular research area which requires attention. Another is a microscopic model of conduction in vitreous solid electrolytes to enhance the thermodynamic macroscopic Weak ~lectrolyte Iheory (WET).

Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com- plex nonlinear systems that cannot be broken down into the behavior of their con- stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many are often highly idealized or time independent.

Proceedings of a NATO ARW held in Sintra, Portugal, March 23-25, 1994

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d' Ampezzo, Italy, between July 25 and August 6, 1993, under the title From Newton to Chaos: Modem Techniques for Understanding and Coping With Chaos inN-Body Dynamical Systems. This institute was the latest in a series of meetings held every three years from 1972 to 1990 in dynamical astronomy, theoretical mechanics and celestial mechanics. The proceedings from these institutes have been well-received in the international community of research workers in these disciplines. The present institute was well attended with 15 series of lectures being given by invited speakers: in addition some 40 presentations were made by the other participants. The majority of these contributions are included in these proceedings. The all-pervading influence of chaos in dynamical systems (of even a few variables) has now been universally recognised by researchers, a recognition forced on us by our ability, using powerful computer hardware and software, to tackle dynamical problems that until twenty-five years ago were intractable. Doubtless it was felt by many that these new techniques provided a break-through in celestial mechanics and its related disciplines. And so they were.

The Cargese Summer School "e;Low Dimensional Applications of Quantum Field Theory"e; was held in July 1995. The School was dedicated to the memory of Claude Itzykson. This session focused on the recent progress in quantum field theory in two dimen- sions with a particular emphasis on integrable models and applications of quantum field theory to condensed matter physics. A large fraction of the school was also devoted to a detailed review of the exciting developments in four dimensional super- symmetric Yang-Mills theory. The diversity of the topics presented constitute, in our opinion, one of the most attractive features of these proceedings. Some contributions constitute a very thor- ough introduction to their subject matter and should be helpful to advanced students in the field while others present entirely new research, not previously published, and should be of considerable interest to the specialist. There were in depth introductory lectures on the application of conformal field theory techniques to disordered systems, on the quantum Hall effect, on quantum in- tegrable systems, on the thermodynamic Bethe Ansatz and on the new developments in supersymmetric gauges theories. The computation of the three point function of the Liouville model using conformal bootstrap methods was presented in detail.

The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "e;Yes,"e; there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.

The aim of this NATO Advanced Study Institute was to bring together scientists and students working in the field of laser matter interactions in order to review and stimulate developmentoffundamental science with ultra-short pulse lasers. New techniques of pulse compression and colliding-pulse mode-locking have made possible the construction of lasers with pulse lengths in the femtosecond range. Such lasers are now in operation at several research laboratories in Europe and the United States. These laser facilities present a new and exciting research direction with both pure and applied science components. In this ASI the emphasis is on fundamental processes occurring in the interaction of short laser pulses with atoms, molecules, solids, and plasmas. In the case of laser-atom (molecule) interactions, high power lasers provide the first access to extreme high-intensity conditions above 10'8 Watts/em', a new frontier for nonlinear interaction of photons with atoms and molecules. New phenomena observed include multiphoton ionization processes, atomic collisions in the presence of a strong laser field, Coulomb explosion following rapid ionization of a molecule and the production of high harmonics of the laser source. Another important topic reviewed in this ASI is the lasercooling ofatoms.

The NATO Advanced Research Workshop "e;Painleve Transcendents, their Asymp- totics and Physical Applications"e;, held at the Alpine Inn in Sainte-Adele, near Montreal, September 2 -7, 1990, brought together a group of experts to discuss the topic and produce this volume. There were 41 participants from 14 countries and 27 lectures were presented, all included in this volume. The speakers presented reviews of topics to which they themselves have made important contributions and also re- sults of new original research. The result is a volume which, though multiauthored, has the character of a monograph on a single topic. This is the theory of nonlinear ordinary differential equations, the solutions of which have no movable singularities, other than poles, and the extension of this theory to partial differential equations. For short we shall call such systems "e;equations with the Painleve property"e;. The search for such equations was a very topical mathematical problem in the 19th century. Early work concentrated on first order differential equations. One of Painleve's important contributions in this field was to develop simple methods applicable to higher order equations. In particular these methods made possible a complete analysis of the equation ;; = f(y',y,x), where f is a rational function of y' and y, with coefficients that are analytic in x. The fundamental result due to Painleve (Acta Math.

The motion of a particle in a random potential in two or more dimensions is chaotic, and the trajectories in deterministically chaotic systems are effectively random. It is therefore no surprise that there are links between the quantum properties of disordered systems and those of simple chaotic systems. The question is, how deep do the connec- tions go? And to what extent do the mathematical techniques designed to understand one problem lead to new insights into the other? The canonical problem in the theory of disordered mesoscopic systems is that of a particle moving in a random array of scatterers. The aim is to calculate the statistical properties of, for example, the quantum energy levels, wavefunctions, and conductance fluctuations by averaging over different arrays; that is, by averaging over an ensemble of different realizations of the random potential. In some regimes, corresponding to energy scales that are large compared to the mean level spacing, this can be done using diagrammatic perturbation theory. In others, where the discreteness of the quantum spectrum becomes important, such an approach fails. A more powerful method, devel- oped by Efetov, involves representing correlation functions in terms of a supersymmetric nonlinear sigma-model. This applies over a wider range of energy scales, covering both the perturbative and non-perturbative regimes. It was proved using this method that energy level correlations in disordered systems coincide with those of random matrix theory when the dimensionless conductance tends to infinity.

Humankind's ever-expanding activities have caused environmental changes that reach beyond localities and regions to become global in scope. Disturbances to the atmosphere, oceans, and land produce changes in the living parts of the planet, while, at the same time, alterations in the biosphere modify the atmosphere, oceans, and land. Understanding this complex web of interactions poses unprecedented intellectual challenges. The atmospheric concentrations of natural trace gases-carbon dioxide (C0 ), methane (CH. ), nitrous oxide (N0), and lower-atmosphere ozone 2 2 (Os)-have increased since the beginning of the industrial revolution. Industrial gases such as the chlorofluorocarbons (CFCs), which are not part of the natural global ecosystem, are increasing at much greater rates than are the naturally occurring trace gases. All these gases absorb and emit infrared radiation and thus have the potential for altering global climate. The major terrestrial biomes are also changing. Although world attention has focused on deforestation, particularly in tropical areas, the development of agriculture, the diversion of water resources, and urbanization have all modified terrestrial ecosystems in both obvious and subtle ways. The terrestrial biosphere, by taking up atmospheric carbon dioxide, acts as a primary determinant of the overall carbon balance of the global ecosystem. Although the ways in which the biosphere absorbs carbon are, as yet, poorly understood, the destruction (and regrowth) of forests certainly alter this process.

The interest in the problem of surface diffusion has been steadily growing over the last fifteen years. This is clearly evident from the increase in the number of papers dealing with the problem, the development of new experimental techniques, and the specialized sessions focusing on diffusion in national and international meetings. Part of the driving force behind this increasing activity is our recently acquired ability to observe and possibly control atomic scale phenomena. It is now possible to look selectively at individual atomistic processes and to determine their relative importance during growth and reactions at surfaces. The number of researchers interested in this problem also has been growing steadily which generates the need for a good reference source to farniliarize newcomers to the problem. While the recent emphasis is on the role of diffusion during growth, there is also continuing progress on the more traditional aspects of the problem describing mass transport in an ensemble of particles. Such a description is based on the statistical mechanical analysis of a collection of particles that mutually interact and develop correlations. An average over the multitude of atomistic processes that operate under these conditions is necessary to fully describe the dynamics in the system.

This volume, the first to specifically address the function of psychologists as practitioners and scientists in medical settings, presents a range of approaches to assessment and diagnostic practice rather than a litany of specific tools, diseases, or diagnostic problems.

Applications in new fields, as for instance the structure of atomic clusters and the marriage of density functional theory with molecular dynamics and simulated annealing, have provided additional impetus to the field of density functional theory.