Hermann Haken

The book offers a novel approach to the study of the complex dynamics of cities. It is based on (1) Synergetics as a science of cooperation and selforganization, (2) information theory including semantic and pragmatic aspects, and optimization principles, (3) a theory of steady state maintenance, and of (4) phase transition, i.e. qualitative changes of structure or behavior. From this novel theoretical vantage point, the book addresses particularly three issues that stand at the core of current discourse on cities: Urban Scaling, Smart Cities and City Planning. An important consequence of “the 21st century as the age of cities”, is that the study of cities currently attracts scientists from a variety of disciplines, ranging from physics, mathematics and computer science, through urban studies, architecture, planning and human geography, to economics, psychology, sociology, public administration and more. The book is thus likely to attract scholars, researchers andstudents of these research domains, of complexity theories of cities, as well as of general complexity theory. In addition, it is directed also to practitioners of urbanism, city planning and urban design.

The book offers a novel approach to the study of the complex dynamics of cities. It is based on (1) Synergetics as a science of cooperation and selforganization, (2) information theory including semantic and pragmatic aspects, and optimization principles, (3) a theory of steady state maintenance, and of (4) phase transition, i.e. qualitative changes of structure or behavior. From this novel theoretical vantage point, the book addresses particularly three issues that stand at the core of current discourse on cities: Urban Scaling, Smart Cities and City Planning. An important consequence of “the 21st century as the age of cities”, is that the study of cities currently attracts scientists from a variety of disciplines, ranging from physics, mathematics and computer science, through urban studies, architecture, planning and human geography, to economics, psychology, sociology, public administration and more. The book is thus likely to attract scholars, researchers andstudents of these research domains, of complexity theories of cities, as well as of general complexity theory. In addition, it is directed also to practitioners of urbanism, city planning and urban design.

This book describes an encompassing modeling approach to psychotherapy, created with the most recent research in the field. Therapeutic interventions are staged within a therapist-client relationship ('alliance'), and become effective by the interplay of deterministic ('causation') and stochastic ('chance') forces. The authors use a Fokker-Planck approach complemented by a structural-mathematical framework from complexity theory. Chapters present statistical tools, which can be applied to analyze the differing time series that depict therapeutic processes. Chapters include examples of how to use these tools within research. The approach adopted in the book – contemporary psychotherapy terminology combined with a systems-theoretical model and algorithms for quantitative psychotherapy research – has the potential to become the new benchmark in psychotherapy. The Process of Psychotherapy is an informative and sophisticated resource for all levels of students, from undergraduate through post-doctoral studies, in the fields of psychology, cognitive psychology, and psychotherapy.

This book describes an encompassing modeling approach to psychotherapy, created with the most recent research in the field. Therapeutic interventions are staged within a therapist-client relationship ('alliance'), and become effective by the interplay of deterministic ('causation') and stochastic ('chance') forces. The authors use a Fokker-Planck approach complemented by a structural-mathematical framework from complexity theory. Chapters present statistical tools, which can be applied to analyze the differing time series that depict therapeutic processes. Chapters include examples of how to use these tools within research. The approach adopted in the book – contemporary psychotherapy terminology combined with a systems-theoretical model and algorithms for quantitative psychotherapy research – has the potential to become the new benchmark in psychotherapy. The Process of Psychotherapy is an informative and sophisticated resource for all levels of students, from undergraduate through post-doctoral studies, in the fields of psychology, cognitive psychology, and psychotherapy.

Die Autoren geben als aktiv Beteiligte erstmalig aus ihrem persönlichen Erleben einen Einblick auf die ersten zwei Jahrzehnte der Synergetik-Geschichte. Hermann Haken führt in die Begrifflichkeit der Synergetik ein und verdeutlicht die Schwierigkeiten, eine neues Denken in der Wissenschaft zu etablieren. Peter Plath geht exemplarisch auf die Vorgeschichte der Synergetik ein und zeigt an einem Fallbeispiel aus der Chemie, wie die Idee der Synergetik zum Leitmotiv einer Forschungsgruppe wurde. Werner Ebeling und Yuri Romanovsky beschreiben die intensive Kooperation der Wissenschaftler aus Ost und West bei der Herausbildung neuer Ideen zur Synergetik.

This monograph demonstrates the interplay between Shannon information and semantic information in cognition. It shows that Shannon’s information acts as driving force for the formation of semantic information; and vice versa, namely, that semantic information participates in the formation of Shannonian information. The authors show that in cognition, Shannonian and semantic information are interrelated as two aspects of a cognitive process termed as information adaptation. In the latter the mind/brain adapts to the environment by the deflating and/or inflating of the information conveyed by the environment. In the process of information adaptation, quantitative variations in Shannon’s information entail different meanings while different meanings affect the quantity of information. The book illustrates the above conceptually and mathematically by reference to three cognitive processes: pattern recognition, face learning and the recognition of a moving object.

Atom- und Quantenphysik führt sorgfältig und leicht verständlich in die Ergebnisse und Methoden der empirischen Atomphysik ein, wobei auch das Rüstzeug der Quantentheorie vermittelt und besonders die Wechselwirkung zwischen Experiment und Theorie herausgearbeitet wird. Die vorliegende achte Auflage enthält neben umfangreichen Aktualisierungen neue Abschnitte zur quantenmechanischen Behandlung des Atoms im Magnetfeld und im elektrischen Feld. Weiter finden sich in dem Kapitel "Fortschritte der Quantenphysik: Tieferes Verständnis und neue Anwendungen" genaue Erläuterungen zur Verschränkung von Wellenfunktionen, dem Einstein-Podolsky-Rosen Paradoxon, den Bellschen Ungleichungen, dem Paradoxon der Schrödingerschen Katze und dem Konzept der Dekohärenz. Das letzte Kapitel führt in die Grundlagen der Quantentheorie der chemischen Bindung ein, welche im zweiten Band der Autoren "Molekülphysik und Quantenchemie" ihre Fortsetzung findet. 177 Übungen mit vollständigen Lösungen runden das Buch ab und dienen der Vertiefung.

Over the past years the field of synergetics has been mushrooming. An ever­ increasing number of scientific papers are published on the subject, and numerous conferences all over the world are devoted to it. Depending on the particular aspects of synergetics being treated, these conferences can have such varied titles as "Nonequilibrium Nonlinear Statistical Physics," "Self-Organization," "Chaos and Order," and others. Many professors and students have expressed the view that the present book provides a good introduction to this new field. This is also reflected by the fact that it has been translated into Russian, Japanese, Chinese, German, and other languages, and that the second edition has also sold out. I am taking the third edition as an opportunity to cover some important recent developments and to make the book still more readable. First, I have largely revised the section on self-organization in continuously extended media and entirely rewritten the section on the Benard instability. Sec­ ond, because the methods of synergetics are penetrating such fields as eco­ nomics, I have included an economic model on the transition from full employ­ ment to underemployment in which I use the concept of nonequilibrium phase transitions developed elsewhere in the book. Third, because a great many papers are currently devoted to the fascinating problem of chaotic motion, I have added a section on discrete maps. These maps are widely used in such problems, and can reveal period-doubling bifurcations, intermittency, and chaos.

This text on the interdisciplinary field of synergetics will be of interest to students and scientists in physics, chemistry, mathematics, biology, electrical, civil and mechanical engineering, and other fields. It continues the outline of basic con­ cepts and methods presented in my book Synergetics. An Introduction, which has by now appeared in English, Russian, J apanese, Chinese, and German. I have written the present book in such a way that most of it can be read in­ dependently of my previous book, though occasionally some knowledge of that book might be useful. But why do these books address such a wide audience? Why are instabilities such a common feature, and what do devices and self-organizing systems have in common? Self-organizing systems acquire their structures or functions without specific interference from outside. The differentiation of cells in biology, and the process of evolution are both examples of self-organization. Devices such as the electronic oscillators used in radio transmitters, on the other hand, are man­ made. But we often forget that in many cases devices function by means of pro­ cesses which are also based on self-organization. In an electronic oscillator the motion of electrons becomes coherent without any coherent driving force from the outside; the device is constructed in such a way as to permit specific collective motions of the electrons. Quite evidently the dividing line between self-organiz­ ing systems and man-made devices is not at all rigid.

This book is a reprint edition that comprises two titles, namely "Synergetics. An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology" and ''Advanced Synergetics. Instability Hierarchies of Self­ Organizing Systems and Devices". The reason for this publication is two-fold: Since synergetics is a new type of interdisciplinary field, initiated by the author in 1969, the basic ideas developed in these volumes are of considerable theoretical interest. But much more than this, the methods and even the concrete examples presented in these books are still highly useful for graduate students, professors, and even for researchers in this fascinating field. The reason lies in the following facts: Synergetics deals with complex systems, i. e. systems that are composed of many individual parts that are able to spontaneously form spatial, temporal or functional structures by means of self-organization. Such phenomena occur in many fields ranging from physics, chemistry and biology to economy and sociology. More recent areas of application have been found in medicine and psychology, where the great potential of the basic principles of synergetics can be unearthed. Further applications have become possible in informatics, for instance the designing of new types of computers, and in other fields of engineering.

It is increasingly being recognized that the experimental and theoretical study of the complex system brain requires the cooperation of many disciplines, in­ cluding biology, medicine, physics, chemistry, mathematics, computer science, linguistics, and others. In this way brain research has become a truly interdis­ ciplinary endeavor. Indeed, the most important progress is quite often made when different disciplines cooperate. Thus it becomes necessary for scientists to look across the fence surrounding their disciplines. The present book is written precisely in this spirit. It addresses graduate students, professors and scientists in a variety of fields, such as biology, medicine and physics. Be­ yond its mathematical representation the book gives ample space to verbal and pictorial descriptions of the main and, as I believe, fundamental new insights, so that it will be of interest to a general readership, too. I use this opportunity to thank my former students, some of whom are my present co-workers, for their cooperation over many years. Among them I wish to mention in particular M. Bestehorn, L. Borland, H. Bunz, A. Daf­ fertshofer, T. Ditzinger, E. Fischer, A. Fuchs, R. Haas, R. Honlinger, V. Jirsa, M. Neufeld, M. Ossig, D. Reimann, M. Schanz, G. Schoner, P. Tass, C. Uhl. My particular thanks go to R. Friedrich and A. Wunderlin for their constant help in many respects. Stimulating discussions with a number of colleagues from a variety of fields are also highly appreciated.

This fourth edition contains a few additional figures. Otherwise only typographical er­ rors have been removed. The final chapter on Fundamentals of the Quantum Theory of Chemical Bonding is continued in an extended way in the textbook Molecular Physics and Elements of Quantum Chemistry by the same authors. This book contains, in particular, a profound presentation of group theory as applied to atoms and molecules. Furthermore, the in­ teraction between atoms and molecules and light is treated in detail. We thank again Springer-Verlag, in particular Dr. H.1. Kblsch and Mr. C.-D. Bachem for their excellent cooperation as always, and Prof. W. D. Brewer for his con­ tinuous support in translating our German text. Stuttgart, February 1994 H. Haken H. C. Wolf Preface to the Third Edition The second edition of this book again enjoyed a very positive reception from both uni­ versity teachers and students. In this edition we have removed all of the typographical errors that came to our attention. In order to keep the book as current as possible, new developments in the direct observation of individual atoms in electromagnetic traps (Paul traps) and of atoms in molecules on solid surfaces using the scanning tunnel microscope have been added to this edition.

Since the publication of the first edition of this book, there have been many im­ portant new developments in the field of molecular physics. The new methods and results which are most significant for students are treated extensively in this second edition. Among these are in particular single-molecule spectroscopy and the field of molecular electronics, which is in a stage of rapid development, including the areas of electroluminescence and organic light-emitting diodes. In addition, we have ex­ tended and corrected the earlier material in a number of places. We have also included exercises in this new edition; they will allow students to deepen their understanding and offer a basis for further individual study. The complete solutions to the exercises can be found on the Internet under www. springeronline. com/3-540-40792-S. We are grateful to Mr. C. -D. Bachem and Dr. Th. Schneider of the Springer­ Verlag for their continuous and very agreeable cooperation during the preparation of the book. We thank our colleague Prof. W. D. Brewer for his competent translation. Stuttgart, February 2004 H. Haken . H. C. Wolf Preface to the First Edition This textbook is intended for use by students of physics, physical chemistry, and theoretical chemistry. The reader is presumed to have a basic knowledge of atomic and quantum physics at the level provided, for example, by the first few chapters in our book The Physics of Atoms and Quanta.

The first edition of this book has found great interest among scientists and en­ gineers dealing with pattern recognition and among psychologists working on psychophysics or Gestalt psychology. This book also proved highly useful for graduate students of informatics. The concept of the synergetic computer offers an important alternative to the by now more traditional neural nets. I just mention a few advantages: There are no ghost states so that time-consuming methods such as simulated annealing can be avoided; the synaptic strengths are explicitly determined by the prototype patterns to be stored, but they can equally well be learned, and the learning procedure allows a classification. Also a precise meaning and function can be attributed to "hidden variables". The synergetic computer has found a number of important practical applications in industry. I use the opportunity of this second edition to include a new section on transfor­ mation properties of the equations of the synergetic computer and on the invariance properties of its order parameter equations. A new section is devoted to the problem of stereopsis that is dealt with by the basic concept of the synergetic computer. Finally, attention is paid to a recent de­ velopment, namely to the use of pulse-coupled neural nets for pattern recognition.

The widespread interest this book has found among professors, scientists and stu­ dents working in a variety of fields has made a new edition necessary. I have used this opportunity to add three new chapters on recent developments. One of the most fascinating fields of modern science is cognitive science which has become a meet­ ing place of many disciplines ranging from mathematics over physics and computer science to psychology. Here, one of the important links between these fields is the concept of information which, however, appears in various disguises, be it as Shan­ non information or as semantic information (or as something still different). So far, meaning seemed to be exorcised from Shannon information, whereas meaning plays a central role in semantic (or as it is sometimes called "pragmatic") information. In the new chapter 13 it will be shown, however, that there is an important interplay between Shannon and semantic information and that, in particular, the latter plays a decisive role in the fixation of Shannon information and, in cognitive processes, al­ lows a drastic reduction of that information. A second, equally fascinating and rapidly developing field for mathematicians, computer scientists and physicists is quantum information and quantum computa­ tion. The inclusion of these topics is a must for any modern treatise dealing with in­ formation. It becomes more and more evident that the abstract concept of informa­ tion is inseparably tied up with its realizations in the physical world.

Brain Dynamics serves to introduce graduate students and nonspecialists from various backgrounds to the field of mathematical and computational neurosciences. Some of the advanced chapters will also be of interest to the specialists. The book approaches the subject through pulse-coupled neural networks, with at their core the lighthouse and integrate-and-fire models, which allow for the highly flexible modelling of realistic synaptic activity, synchronization and spatio-temporal pattern formation. Topics also include pulse-averaged equations and their application to movement coordination. The book closes with a short analysis of models versus the real neurophysiological system. The second edition has been thoroughly updated and augmented by two extensive chapters that discuss the interplay between pattern recognition and synchronization. Further, to enhance the usefulness as textbook and for self-study, the detailed solutions for all 34 exercises throughout the text have been added.

The highly positive affirmation and wide reception that this book continues to receive from professors and students ahke is the occasion for this 7th edition. Once again we have included a number of valuable suggestions for improvements, which we address as appropriate. In addition, we refer to a number of developments in atomic physics. Of these new developments in regard to exotic atoms, we mention antihydrogen in par­ ticular, because fundamental experiments in matter and antimatter can be expected in the future. Furthermore, we have inserted a chapter on the behaviour of atoms in strong elec­ trical fields. Experiments with corresponding lasers could only recently be realized. We thank our Jenaer colleague, R. Sauerbrey, for his contribution of this chapter. We have also included a new chapter on the behaviour of the hydrogen atom in strong magnetic fields. The results are of profound interest for two very different fields of physics: on the one hand, according to classical physics, one expects chaotic behaviour from Rydberg atoms in magnetic fields that can be created in the laborato­ ry; thus, an association can be drawn to aspects of chaos theory and the problems of quantum chaos. On the other hand, the very strong fields necessary for low quantum numbers are realized in the cosmos, in particular with white dwarfs and neutron stars.

Brain Dynamics serves to introduce graduate students and nonspecialists from various backgrounds to the field of mathematical and computational neurosciences. Some of the advanced chapters will also be of interest to the specialists. The book approaches the subject through pulse-coupled neural networks, with at their core the lighthouse and integrate-and-fire models, which allow for the highly flexible modelling of realistic synaptic activity, synchronization and spatio-temporal pattern formation. Topics also include pulse-averaged equations and their application to movement coordination. The book closes with a short analysis of models versus the real neurophysiological system. The second edition has been thoroughly updated and augmented by two extensive chapters that discuss the interplay between pattern recognition and synchronization. Further, to enhance the usefulness as textbook and for self-study, the detailed solutions for all 34 exercises throughout the text have been added.