While basic features of polarons were well recognized a long time ago and have been described in a number of review papers and textbooks, interest in the role of electron-phonon interactions and polaron dynamics in di?- ent materials has recently gone through a vigorous revival. Electron-phonon interactions have been shown to be relevant in many inorganic and organic semiconductors and polymers, colossal magnetoresistance oxides, and tra- port through nanowires and quantum dots also often depends on vibronic displacements of ions. These interactions presumably play a role in hi- temperature superconductors as well. The continued interest in polarons extends beyond the physical description of advanced materials. The ?eld has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational methods, exact diagonalization, Quantum Monte Carlo, and other techniques. This book reviews some recent developments in the ?eld of polarons, starting with the basics and covering a number of active directions of research. Single- and multipolaron theories have o?ered more insight into colossal magnetoresistance and in a broad spectrum of ph- ical properties of structures with reduced dimension and dimensionality such as transport, optical absorption, Raman scattering, photoluminescence, magneto-optics, etc. While nobody - at present - has a ?nal theory of hi- temperature superconductivity, we discuss one alternative (polaronic) route. We have bene?ted from discussions with many experts in the ?eld.

The Advanced Study Institute on "Theoretical Aspects and New Developments in Magneto-Optics" was held at the University of Antwerpen (R.U.C.A.), from July 16 to July 28, 1979. The Institute was sponsored by NATO. Co-sponsors were: Agfa-Gevaert (Belgium), A.S.L.K. (Belgium), Bell Telephone Mfg. CO. (Belgium), Esso Belgium, Generale Bankmaatschappij (Belgium), General Motors (Belgium), I.B.M. (Belgium), Kredietbank (Belgium), Metallurgie Hoboken-Over pelt (Belgium), National Science Foundation (U.S.A). A total of 60 lecturers and participants attended the Institute. Scope of the Institute The magneto-optic phenomena are due to the change of the polarizability of a substance as a result of the splitting of the quantized energy bands. Most of these phenomena were discovered during the second half of this century. The understanding of the magneto-optical effects of all kinds, however, was brought by the advent of quantum mechanics, and since then important progress has been made in many fields of experimental methods and techniques."

The International Workshop on "The Use of Supercomputers in Theoretical Science" took place on January 24 and 25, 1991, at the University of Antwerp (UIA), Antwerpen, Belgium. It was the sixth in a series of workshops, the fIrst of which took place in 1984. The principal aim of these workshops is to present the state of the art in scientific large-scale and high speed-computation. Computational science has developed into a third methodology equally important now as its theoretical and experimental companions. Gradually academic researchers acquired access to a variety of supercomputers and as a consequence computational science has become a major tool for their work. It is a pleasure to thank the Belgian National Science Foundation (NFWO-FNRS) and the Ministry of ScientifIc Affairs for sponsoring the workshop. It was organized both in the framework of the Third Cycle "Vectorization, Parallel Processing and Supercomputers" and the "Governemental Program in Information Technology." We also very much would like to thank the University of Antwerp (Universitaire Instelling Antwerpen -VIA) for fInancial and material support. Special thanks are due to Mrs. H. Evans for the typing and editing of the manuscripts and for the preparation of the author and subject indexes. J.T. Devreese P.E. Van Camp University of Antwerp July 1991 v CONlENTS High Perfonnance Numerically Intensive Applications on Distributed Memory Parallel Computers .................... . F.W. Wray Abstract ......................................... .

The Advanced Study Institute on "Path Integrals and Their Applications in Quantum, Statistical, and Solid State Physics" was held at the University of Antwerpen (R.U.C.A.), July 17-30, 1977. The Institute was sponsored by NATO. Co-sponsors were: A.C.E.C. (Belgium), Agfa-Gevaert (Belgium), l'Air Li~uide BeIge (Belgium), Be1gonucleaire (Belgium), Bell Telephone Mfg. Co. (Belgium), Boelwerf (Belgium), Generale BankmaatschappiJ (Belgium), I.B.M. (Belgium), Kredietbank (Belgium), National Science Foundation (U.S.A.), Siemens (Belgium). A total of 100 lecturers and partici- pants attended the Institute. The development of path (or functional) integrals in relation to problems of stochastic nature dates back to the early 20's. At that time, Wiener succeeded in obtaining the fundamental solution of the diffusion e~uation using Einstein's joint probability of finding a Brownian particle in a succession of space intervals during a corresponding succession of time intervals. Dirac in the early 30's sowed the seeds of the path integral formulation of ~uantum mecha- nics. However, the major and decisive step in this direction was taken with Feynman's works in ~uantum and statistical physics, and quantum electrodynamicso The applications now extend to areas such as continuous mechanics, and recently functional integration methods have been employed by Edwards for the study of polymerized matter.

The Advanced Study Institute on "Theoretical Aspects and New Developments in Magneto-Optics" was held at the University of Antwerpen (R.U.C.A.), from July 16 to July 28, 1979. The Institute was sponsored by NATO. Co-sponsors were: Agfa-Gevaert (Belgium), A.S.L.K. (Belgium), Bell Telephone Mfg. CO. (Belgium), Esso Belgium, Generale Bankmaatschappij (Belgium), General Motors (Belgium), I.B.M. (Belgium), Kredietbank (Belgium), Metallurgie Hoboken-Over pelt (Belgium), National Science Foundation (U.S.A). A total of 60 lecturers and participants attended the Institute. Scope of the Institute The magneto-optic phenomena are due to the change of the polarizability of a substance as a result of the splitting of the quantized energy bands. Most of these phenomena were discovered during the second half of this century. The understanding of the magneto-optical effects of all kinds, however, was brought by the advent of quantum mechanics, and since then important progress has been made in many fields of experimental methods and techniques.

The International Workshop on "The Use of Supercomputers in Theoretical Science" took place on January 24 and 25, 1991, at the University of Antwerp (UIA), Antwerpen, Belgium. It was the sixth in a series of workshops, the fIrst of which took place in 1984. The principal aim of these workshops is to present the state of the art in scientific large-scale and high speed-computation. Computational science has developed into a third methodology equally important now as its theoretical and experimental companions. Gradually academic researchers acquired access to a variety of supercomputers and as a consequence computational science has become a major tool for their work. It is a pleasure to thank the Belgian National Science Foundation (NFWO-FNRS) and the Ministry of ScientifIc Affairs for sponsoring the workshop. It was organized both in the framework of the Third Cycle "Vectorization, Parallel Processing and Supercomputers" and the "Governemental Program in Information Technology." We also very much would like to thank the University of Antwerp (Universitaire Instelling Antwerpen -VIA) for fInancial and material support. Special thanks are due to Mrs. H. Evans for the typing and editing of the manuscripts and for the preparation of the author and subject indexes. J.T. Devreese P.E. Van Camp University of Antwerp July 1991 v CONlENTS High Perfonnance Numerically Intensive Applications on Distributed Memory Parallel Computers .................... . F.W. Wray Abstract ......................................... .

The 1984 Advanced Study Institute on "Electronic Structure, Dynamics and Quantum Structural Properties of Condensed Matter" took place at the Corsendonk Conference Center, close to the City of Antwerpen, from July 16 till 27, 1984. This NATO Advanced Study Institute was motivated by the research in my Institute, where, in 1971, a project was started on "ab-initio" phonon calculations in Silicon. I~ is my pleasure to thank several instances and people who made this ASI possible. First of all, the sponsor of the Institute, the NATO Scientific Committee. Next, the co-sponsors: Agfa-Gevaert, Bell Telephone Mfg. Co. N.V., C & A, Esso Belgium*, CDC Belgium, Janssens Pharmaceutica, Kredietbank and the Scientific Office of the U.S. Army. Special thanks are due to Dr. P. Van Camp and Drs. H. Nachtegaele, who, over several months, prepared the practical aspects of the ASI with the secretarial help of Mrs. R.-M. Vandekerkhof. I also like to. thank Mrs. M. Cuyvers who prepared and organized the subject and material index and Mrs. H. Evans for typing-assist ance. I express particular gratitude to Mrs. F. Nedee, who, like in 1981 and 1982, has put the magnificent Corsendonk Conference Center at our disposal and to Mr. D. Van Der Brempt, Director of the Corsendonk Conference Center, for the efficient way in which he and his staff took care of the practical organization at the Conference Center.

The 1986 Advanced Study Institute on "The Physics of the two-Dimen sional Electron Gas" took place at the Conference Centre liTer Helme," close to Oostende (Belgium), from June 2 till 16, 1986. We were motivated to organize this Advanced Study Institute in view of the recent experimental and theoretical progress in the study of the two-dimensional electron gas. An additional motivation was our own theore tical interest in cyclotron resonance in two-dimensional electron systems at our institute. It is my pleasure to thank several instances and people who made this Advanced Study Institute possible. First of all, the sponsor of the Advanced Study Institute, the NATO Scientific Committee. Furthermore, the co sponsors: Agfa Gevaert, Bell Telephone Mfg. Co. N.V., Burroughs Belgium. Control Data. Digital Equipment Corporation, Esso Belgium. European Research Office (USA). Kredietbank. National Science Foundation (USA). Special thanks are due to the members of the Program Committee and the members of the Organizing Committee. I would also like to thank Mrs. H. Evans for typing assistance."

The Advanced Study Institute on 'Elementary Excitations in Solids, Molecules, and Atoms' was held at the University of Antwerp (U.I.A.) from June 18th till June 30th 1973. The In stitute was sponsored by NATO. Co-sponsors were: Agfa-Gevaert N.V. (Mortsel - Belgium), Bell Telephone Mfg. Co. (Antwerp Belgium), the National Science Foundation (Washington D.C. - U.S.A.) and the University of Antwerp (U.I.A.). A total of 120 lecturers and participants attended the Institute. Over the last few years, substantial progress has been made in the description of the elementary excitations of the elec tronic and vibrational systems and their interactions. Parallel with this, the experimentalists have obtained outstanding re sults, partly as a result of availability of coherent light sour ces from the far infrared through the visible region, and partly because of the availability of synchrotron radiation sources in the soft X-ray region. The results of today will lead to fur ther progress over the next years. It was the purpose of this NATO Advanced Study Institute to present astate of the art, namely a survey of experiment and theory."

These volumes contain the invited and contributed talks of the first general Conference of the Condensed Matter Division of the European Physical Society, which took place at the campus of the University of Antwerpen (Universitaire Instelling Antwerpen) from April 9 till 11, 1980. The invited talks give a broad perspective of the current state in Europe of research in condensed matter physics. New developments and advances in experiments as well as theory are reported for 28 topics. Some of these developments, such as the recent stabilization of mono-atomic hydrogen, with the challenging prospect of Bose condensation, can be considered as major break throughs in condensed matter physics. Of the 65 invited lecturers, 54 have submitted a manuscript. The remaining talks are published as abstracts. The contents of this first volume consists of 9 plenary papers. Among the topics treated in these papers are: - electronic structure computations of iron the density functional theory hydrogen in amorphous si topologically disordered materials nuclear antiferromagnetism stabilization of mono-atomic hydrogen gas covalent and metallic glasses nonlinear excitations in ferroelectrics."

These volumes contain the invited and contributed talks of the first general Conference of the Condensed Matter Division of the European Physical Society, which took place at the campus of the University of Antwerpen (Universitaire Instelling Antwerpen) from April 9 till 11, 1980. The invited talks give a broad perspective of the current state in Europe of research in condensed matter physics. New developments and advances in experiments as well as theory are reported for 28 topics. Some of these developments, such as the recent stabilization of mono-atomic hydrogen, with the challenging prospect of Bose condensation, can be considered as major break throughs in condensed matter physics. Of the 65 invited lecturers, 54 have submitted a manuscript. The remaining talks are published as abstracts. The contents of this first volume consists of 9 plenary papers. Among the topics treated in these papers are: - electronic structure computations of iron the density functional theory hydrogen in amorphous Si topologically disordered materials nuclear antiferromagnetism stabilization of mono-atomic hydrogen gas covalent and metallic glasses nonlinear excitations in ferroelectrics.

These volumes contain the invited and contributed talks of the first general Conference of the Condensed Matter Division of the European Physical Society, which took place at the campus of the University of Antwerpen

The 1982 Antwerp Advanced Study Institute on "Physics of Polarons and Excitons in Polar Semiconductors and Ionic Crystals" took place from July 26 till August 5 at the Conference Center Priorij Corsen donk, a restored monastery, close to the city of Antwerp. It was the seventh Institute in our series which started in 1971. This Advanced Study Institute, which was held fifty years after Landau introduced the polaron concept, can be considered as the third major international symposium devoted to the physics of pola rons. The first such symposium took place in St. Andrews in 1962 under the title "Polarons and Excitons" [I]. The early theoretical developments related to polarons were reviewed in depth at this meeting; the derivation of the polaron hamiltonian by Frohlich, the Frohlich weak coupling theory (and the equivalent weak coupling canonical transformations), the Landau-Pekar and Bogolubov strong coupling theory and the Feynman polaron model formulated with his path integrals. The main emphasis was on the polaron self-energy, effective mass and mobility. From the experimental side the first evidence for polaron effects was provided by the pioneering cyclotron and mobility measurements o~ the silver halides by F. e. Brown and his group. Also the significance of polaron effects for the under standing of excitons in ionic crystals was a central topic in St. Andrews. The second Advanced Study Institute concerning polaron physics was organized at the University of Antwerp (R. U. C. A.

Although the problem of a metal in one dimension has long been known to solid-state physicists, it was not until the synthesis of real one-dimensional or quasi-one-dimensional systems that this subject began to attract considerable attention. This has been due in part to the search for high temperature superconductivity and the possibility of reaching this goal with quasi-one-dimensional substances. A period of intense activity began in 1973 with the report of a measurement of an apparently divergent conduc tivity peak in TfF-TCNQ. Since then a great deal has been learned about quasi-one-dimensional conductors. The emphasis now has shifted from trying to find materials of very high conductivity to the many interesting problems of physics and chemistry involved. But many questions remain open and are still under active investigation. This book gives a review of the experimental as well as theoretical progress made in this field over the last years. All the chapters have been written by scientists who have established themselves as experts in theoreti cal and experimental solid-state physics. The book is intended to be of use both to students and researchers entering the field as well as to more advanced physicists. The wealth of ideas and information it contains ought to be useful to anyone interested in quasi-one-dimensional systems, organic solids, or the search for novel conduction and superconduction mechanisms. The editors are very grateful to the authors for their collaboration in this book."

The International Workshop on "The Use of Supercomputers in Theoretical Science" took place on November 29 and 30, 1989 at the University of Antwerp (UIA), Antwerpen, Belgium. It was the fifth in a series of workshops, the first of which took place in 1984. The principal aim of these workshops is to present the state-of-the-art in scientific large scale and high speed computation. Computational science has developed into a third methodology equally important now as its theoretical and experimental companions. Gradually academic researchers acquired access to a variety of supercomputers and as a consequence computational science has become a major tool for their work. It is a pleasure to thank the Belgian National Science Foundation (NFWO-FNRS) and the Ministry of Scientific Affairs for sponsoring the workshop. It was organized both in the framework of the Third Cycle "Vectorization, Parallel Processing and Supercomputers" and the "Governemental Program in Information Technology"~ We also very much would like to thank the University of Antwerp (Universitaire Instelling Antwerpen - UIA) for financial and material support. Special thanks are due to Mrs. H. Evans for the typing and editing of the manuscripts and for the preparation of the author and subject index.

The International Workshops on "The Use of Supercomputers in Theoretical Science" have become a tradition at the Univer sity of Antwerp, Belgium. The first one took place in 1984. This volume combines the proceedings of the second work shop (December 12, 1985), of the third (June 16, 1987) and of the fourth (June 9, 1988). The principal aim of the International Workshops is to present the state-of-the-art in scientific high speed computa tion. Indeed, during the past ten years computational science has become a third methodology with merits equal to the theo retical and experimental sciences. Regretfully, access to supercomputers remains limited for academic researchers. None theless, supercomputers have become a major tool for scientists in a wide variety of scientific fields, and they lead to a realistic solution of problems that could not be solved a decade ago. It is a pleasure to thank the Belgian National Science Foundation (NFWO-FNRS) for the sponsoring of all the workshops. These workshops are organized in the framework of the Third Cy cle "Vectorization, Parallel Processing and Supercomputers," which is also funded by the NFWO-FNRS. The other sponsor I want to thank is the University of Antwerp, where the workshops took place. The University of Antwerp (UIA), together with the NFWO-FNRS, are also the main sponsors of the ALPHA-project, which gives the scientists of Belgium the opportunity to obtain an easy supercomputer connection."

From July 20 till 31, 1981, the Advanced Study Institute on "Electron Correlations in Solids, Molecules and Atoms," sponsored by NATO, was held at the University of Antwerpen (U.I.A.), in the Conference Center Corsendonk. In the last few years, the problem of many-electron correlations has gained renewed attention, due to recent experimental and theoretic al developments. From the theoretical point of view, more sophisticated treatments of the homogeneous electron gas model evolved, including dynamical aspects of the electron correlation in the dielectric response. Furthermore, the homogeneous electron gas, which served as a model for simple metals, was extended to include spin- and charge-density waves and phasons. The concept of elementary excitations too was introduced not only in perfectly ordered metallic crystals, but also in magnetic alloys, in liquid metals and alloys, in semiconductors, and even in molecules and atoms. Fairly accurate quantitative calculations of these effects recently became possible, ranging from plasmon frequencies in atoms, over dielectric response of semiconduc tors and resistivity in magnetic alloys to electron-hole liquids and their phase separation. The recent technological evolution allowed for more accurate measurements in previously unaccessible domains, e.g. X-ray scatter ing and fast electron energy loss at large wavevector. Moreover, these new developments opened new perspectives in physics, accompany ing or even introducing the new concepts which also evolved in the theory."

The International Workshop on "The Use of Super computers in Theoretical Science" took place from July 30 till August 1, 1984, at the Conference Center of the "Priorij Corsendonk", close to the city of Antwerpen, Belgium. During the past decade computational science has developed itself to a third methodology besides the experimental and theoretical sciences. This remarkable evolution was only possible due to a drastic increase of the computational power of present day computers. Indeed, computational physics and chemistry as such is certainly not new, but it was only during the past ten years or so that realistic problems could be solved numerically to a sufficient degree of accuracy. During this workshop the state-of-the-art in high speed computation was presented by a team of lecturers who are well known for their competence in this field. It is a pleasure to thank several organizations and companies who made this workshop possible. First of all, the main sponsors: the Belgian National Science Found ation (NFWO-FNRS) and the "Universitaire Instelling Ant werpen". Next, the co-sponsors: Agfa-Gevaert N. V., Control Data Belgium and the Belgian Ministry of Education. Special thanks are due to Dr. P.E. Van Camp and Drs. H. Nachtegaele for the practical organization of this workshop. I would also like to thank Mrs. H. Evans for typing the manuscripts and for preparing the author and subject index. v Last but not least I express my gratitude to Mr.

This volume contains of the proceedings of the CECAM {Centre d'Etudes de Calcul Atomique et Moleculaire} workshop on "Ab Initio Calculation of Phonon Spectra" which took place at the campus of the University of Antwerpen (Universitaire Instelling Antwerpen) on June 4 and 5, 1981. This workshop was sponsored by the Universitaire Instelling Antwerpen, by the Belgian "Nationaal Fonds voor Weten- schappelijk Onderzoek" and the Belgian Ministry of Education and Cultural Affairs. Although the calculation of phonon spectra in a solid has long been known to solid state physicists, it is only in the last decade that a macroscopic theory which treats the response of the electrons to the vibrations of the ions has been developed in a successful way. In the case of semiconductors numerical calculations of phonon frequencies were not performed until very recently due to the complex- ity of the problem. The correct treatment of the electron in the crystal has also led to an investigation of electron-phonon inter- action, including many body effects. Success has been achieved in the calculation of phonon anomalies and the coupling parameters in transition metals. In the case of surfaces the conductions for the appearance of electronic instabilities and the coupling of the resulting charge density wave to the lattice have been studied.

While basic features of polarons were well recognized a long time ago and have been described in a number of review papers and textbooks, interest in the role of electron-phonon interactions and polaron dynamics in di?- ent materials has recently gone through a vigorous revival. Electron-phonon interactions have been shown to be relevant in many inorganic and organic semiconductors and polymers, colossal magnetoresistance oxides, and tra- port through nanowires and quantum dots also often depends on vibronic displacements of ions. These interactions presumably play a role in hi- temperature superconductors as well. The continued interest in polarons extends beyond the physical description of advanced materials. The ?eld has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational methods, exact diagonalization, Quantum Monte Carlo, and other techniques. This book reviews some recent developments in the ?eld of polarons, starting with the basics and covering a number of active directions of research. Single- and multipolaron theories have o?ered more insight into colossal magnetoresistance and in a broad spectrum of ph- ical properties of structures with reduced dimension and dimensionality such as transport, optical absorption, Raman scattering, photoluminescence, magneto-optics, etc. While nobody - at present - has a ?nal theory of hi- temperature superconductivity, we discuss one alternative (polaronic) route. We have bene?ted from discussions with many experts in the ?eld.

The interviews in this book span over twenty years, over two decades. For years I went with my recording device to tournaments like Wijk aan Zee, Frankfurt Chess Classic, Hoogeveen... often to interview the interesting player of the moment in some hotel bar or quiet interview room. 31 out of the 35 interviews came about this way. That is... until March 2020, when out of nowhere, covid broke out. Suddenly chess tournaments were no longer held and a live interview with chess players was no longer possible.