A forest-fire model is introduced which contains a lightning probability f. This leads to a selforganized critical state in the limit f 0 provided that the time scales of tree growth and burning down of forest clusters are separated. %e derive scaling laws and calculate all critical exponents. The values of the critical exponents are confirmed by computer simulations. For a two-dimensional system, we show that the forest density in the critical state assumes its minimum possible value, i.e. , that energy dissipation is maximum.

We discuss the properties of a self{organized critical forest{ re model which has been introduced recently. We derive scaling laws and de ne critical exponents. The values of these critical exponents are determined by computer simulations in 1 to 8 dimensions. The simulations suggest a critical dimension dc = 6 above which the critical exponents assume their mean{ eld values. Changing the lattice symmetry and allowing trees to be immune against re, we show that the critical exponents are universal.

This is a textbook on quantum mechanics. In an introductory chapter, the basic postulates are established, beginning with the historical development, by the analysis of an interference experiment. From then on the organization is purely deductive. In addition to the basic ideas and numerous applications, new aspects of quantum mechanics and their experimental tests are presented.In the text, emphasis is placed on a concise, yet self-contained, presentation. The comprehensibility is guaranteed by giving all mathematical steps and by carrying out the intermediate calculations completely and thoroughly.The book treats nonrelativistic quantum mechanics without second quantization, except for an elementary treatment of the quantization of the radiation field in the context of optical transitions. Aside from the essential core of quantum mechanics, within which scattering theory, time dependent phenomena, and the density matrix are thoroughly discussed, the book presents the theory of measurement and the Bell inequality. The penultimate chapter is devoted to supersymmetric quantum mechanics, a topic which to date has only been accessible in the research literature.For didactic reasons, we begin with wave mechanics; from Chap. 8 on we introduce the Dirac notation. Intermediate calculations and remarks not essential for comprehension are presented in small print. Only in the somewhat more advanced sections are references given, which, even there, are not intended to be complete, but rather to stimulate further reading. Problems at the end of the chapters are intended to consolidate the student's knowledge.The book is recommended to students of physics and related areas with some knowledge of mechanics and classical electrodynamics, and we hope it will augment teaching material already available.This book came about as the result of lectures on quantum mechanics given by the author since 1973 at the University of Linz and the Technical University of Munich. Some parts of the original rough draft, figures, and tables were completed with the help of R. Alkofer, E. Frey, and H.-T. Janka. Careful reading of the proofs by Chr. Baumgiirlel, R. Eckl, N. Knoblauch, J. Krumrey, w. Rossmann-Bloeck and M. Zobel ensured the factual accuracy of the translation. W. Gasser read the entire manuscript and made useful suggestions about many of the chapters of the book. Here, I would like to express my sincere gratitude to them, to Mrs. H. Sprzagalla for typing the original manuscript, and to all my other colleagues who gave important assistance in producing this book, as well as to the publisher.

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of the initial conditions and without fine-tuning of the parameters.After an introduction, we define the rules of the model and discuss various large-scale structures which may appear in this system. The origin of the critical behavior is explained, critical exponents are introduced, and scaling relations between the exponents are derived. Results of computer simulations and analytical calculations are summarized. The existence of an upper critical dimension and the universality of the critical behavior under changes of lattice symmetry or the introduction of immunity are discussed. A survey of interesting modifications of the forest-fire model is given. Finally, several other important SOC models are briefly described.

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We review our current understanding of the critical dynamics of magnets above and below the transition temperature with focus on the effects due to the dipole-dipole interaction present in all real magnets. Significant progress in our understanding of real ferromagnets in the vicinity of the critical point has been made in the last decade through improved experimental techniques and theoretical advances in taking into account realistic spin-spin interactions. We start our review with a discussion of the theoretical results for the critical dynamics based on recent renormalization group, mode coupling and spin-wave theories. A detailed comparison is made ot~ the theory with experimental results obtained by different measuring techniques, such as neutron scattering, hyperfine interaction, muon spin resonance, electron spin resonance, and magnetic relaxation, in various materials. Furthermore we discuss the effects of dipolar interaction on the critical dynamics of three-dimensional isotropic antiferromagnets and uniaxial ferromagnets. Special attention is also paid to a discussion of the consequences of dipolar anisotropies on the existence of magnetic order and the spin-wave spectrum in two-dimensional ferromagnets and antiferromagnets. We close our review with a formulation of critical dynamics in terms of nonlinear Langevin equations.

This is a textbook on quantum mechanics. In an introductory chapter, the basic postulates are established, beginning with the historical development, by the analysis of an interference experiment. From then on the organization is purely deductive. In addition to the basic ideas and numerous applications, new aspects of quantum mechanics and their experimental tests are presented. In the text, emphasis is placed on a concise, yet self-contained, presentation. The comprehensibility is guaranteed by giving all mathematical steps and by carrying out the intermediate calculations completely and thoroughly.The book treats nonrelativistic quantum mechanics without second quantization, except for an elementary treatment of the quantization of the radiation field in the context of optical transitions. Aside from the essential core of quantum mechanics, within which scattering theory, time-dependent phenomena, and the density matrix are thoroughly discussed, the book presents the theory of measurement and the Bell inequality. The penultimate chapter is devoted to supersymmetric quantum mechanics, a topic which to date has only been accessible in the research literature.For didactic reasons, we begin with wave mechanics; from Chap. 8 on we introduce the Dirac notation. Intermediate calculations and remarks not essential for comprehension are presented in small print. Only in the somewhat more advanced sections are references given, which even there, are not intended to be complete, but rather to stimulate further reading. Problems at the end of the chapters are intended to consolidate the student's knowledge.The book is recommended to students of physics and related areas with some knowledge of mechanics and classical electrodynamics, and we hope it will augment teaching material already available.This book came about as the result of lectures on quantum mechanics given by the author since 1973 at the University of Linz and the Technical University of Munich. Some parts of the original rough draft, figures, and tables were completed with the help of R. Alkover, E. Frey and H.-T. Janka. Careful reading of the proofs by Chr. Baumgartel, R. Eckl, N. Knoblauch, J. Krumrey and W. Rossmann-Bloeck ensured the factual accuracy of the translation. W. Gasser read the entire manuscript and made useful suggestions about many of the chapters of the book. Here, I would like to express my sincere gratitude to them, and to all my other colleagues who gave important assistance in producing this book, as well as to the publisher.

A theory of periodic multilayers consisting of two alternating ferromagnetic materials with different transition temperatures is presented. The theory is based on an inhomogeneous Ginzburg-Landau (GL) functional, where the GL coefficients are chosen to model the alternating layers and interface interactions. The transition temperature of the composite material is derived by use of the linear stability analysis of the inhomogeneous GL functional. The static magnetization profiles for different temperatures are calculated analytically. It is shown that the magnetization penetrating into the low-temperature ferromagnet falls off inversely with distance close to T& and exponentially far above Tl, where Ti is the 1ower transition temperature. We also consider the average magnetization of this multilayer system and its characteristic temperature dependence. The spin dynamics are studied by use of a generalized Bloch equation. Different limiting cases as well as the general situation with both dipolar and exchange interactions are considered. The magnon dispersion relation is computed and by symmetry considerations, it is shown that the gaps vanish at certain values of the wave vector k. The inelastic neutron scattering cross section is calculated.With appropriate modifications the theory can be applied to other systems undergoing phase transitions, such as ferroelectrics.