Bøger af Hermann Haken

A thorough knowledge of the physics of atoms and quanta is clearly a must for every student of physics but also for students of neighbouring disciplines such as chemistry and electrical engineering. What these students especially need is a coherent presenta- tion of both the experimental and the theoretical aspects of atomic and quantum physics. Indeed, this field could evolve only through the intimate interaction between ingenious experiments and an equally ingenious development of bold new ideas. It is well known that the study of the microworld of atoms caused a revolution of physical thought, and fundamental ideas of classical physics, such as those on measur- ability, had to be abandoned. But atomic and quantum physics is not only a fascinating field with respect to the development of far-reaching new physical ideas. It is also of enormous importance as a basis for other fields. For instance, it provides chemistry with a conceptual basis through the quantum theory of chemical bonding. Modern solid-state physics, with its numerous applications in communication and computer technology, rests on the fundamental concepts first developed in atomic and quantum physics. Among the many other important technical applications we mention just the laser, a now widely used light source which produces light whose physical nature is quite different from that of conventional lamps. In this book we have tried to convey to the reader some of the fascination which atomic and quantum physics still gives a physicist studying this field.

The spontaneous formation of well organized structures out of germs or even out of chaos is one of the most fascinating phenomena and most challenging problems scientists are confronted with. Such phenomena are an experience of our daily life when we observe the growth of plants and animals. Thinking of much larger time scales, scientists are led into the problems of evolution, and, ultimately, of the origin of living matter. When we try to explain or understand in some sense these extremely complex biological phenomena it is a natural question, whether pro- cesses of self-organization may be found in much simpler systems of the un- animated world. In recent years it has become more and more evident that there exist numerous examples in physical and chemical systems where well organized spatial, temporal, or spatio-temporal structures arise out of chaotic states. Furthermore, as in living of these systems can be maintained only by a flux of organisms, the functioning energy (and matter) through them. In contrast to man-made machines, which are to exhibit special structures and functionings, these structures develop spon- devised It came as a surprise to many scientists that taneously-they are self-organizing. numerous such systems show striking similarities in their behavior when passing from the disordered to the ordered state. This strongly indicates that the function- of such systems obeys the same basic principles. In our book we wish to explain ing such basic principles and underlying conceptions and to present the mathematical tools to cope with them.

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.

Complex systems are ubiquitous, and practically all branches of science ranging from physics through chemistry and biology to economics and sociology have to deal with them. In this book we wish to present concepts and methods for dealing with complex systems from a unifying point of view. Therefore it may be of inter- est to graduate students, professors and research workers who are concerned with theoretical work in the above-mentioned fields. The basic idea for our unified ap- proach sterns from that of synergetics. In order to find unifying principles we shall focus our attention on those situations where a complex system changes its macroscopic behavior qualitatively, or in other words, where it changes its macroscopic spatial, temporal or functional structure. Until now, the theory of synergetics has usually begun with a microscopic or mesoscopic description of a complex system. In this book we present an approach which starts out from macroscopic data. In particular we shall treat systems that acquire their new structure without specific interference from the outside; i. e. systems which are self-organizing. The vehicle we shall use is information. Since this word has several quite different meanings, all of which are important for our purpose, we shall discuss its various aspects. These range from Shannon information, from which all semantics has been exorcised, to the effects of information on receivers and the self-creation of meaning.

Synergetics may be considered as an interdisciplinary effort dealing with the gene- ral problem of how science can cope with complex systems. The preceding symposia on synergetics were devoted to systems of physics, chemistry and partly also biolo- gy and sociology. It was possible to develop adequate concepts to describe and even to calculate evolving macroscopic spatial, temporal, and functional structures which emerge through self-organization of the individual parts of the systems under con- sideration. This book contains the invited papers presented at the Symposium on the Synerge- tics of the brain, Schloss Elmau, Bavaria, May 2 to 7, 1983. The inclusion of this topic in the synergetics enterprise represents a big step towards a treatment of complex systems. Most probably the human brain is the most complex system we know of. As the organizers believe, this symposium provides the reader with a good cross section of experimental results and theoretical approaches to cope with the complex problems of structure and function of the brain. It was generally felt that such a joint meeting between experimentalists and theoreticians is of great importance for future development of this field. Modern experimental methods, e. g. multielectrode derivations allow or will allow us, in short, to collect huge amounts of data. Simi- larly high-speed computers will flood us with an enormous number of outputs once the basic model equations have been chosen.

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 "e;hidden variables"e;. 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.

This monograph demonstrates the interplay between Shannon information and semantic information in cognition. In the process of information adaptation, quantitative variations in Shannon's information entail different meanings while different meanings affect the quantity of information.

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.

This book, written by one of the pioneers of laser theory, is now considered a classic by many laser physicists. It presents a thorough treatment of the theory of laser resonators, the quantum theory of coherence, and the quantization of electromagnetic fields.

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.

This book presents a novel approach to neural nets and thus offers a genuine alternative to the hitherto known neuro-computers. The new edition includes a section on transformation properties of the equations of the synergetic computer and on the invariance properties of the order parameter equations.

Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made.

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;