Physics of Long-Range Interacting Systems [Hardcover]

An upper-level text on the physics of long-range interactions. The first two parts describe the theoretical and computational instruments needed to study both the equilibrium and dynamical properties of systems subject to long-range forces. The third part is devoted to applications of such techniques to the most relevant examples of such systems.This book deals with an important class of many-body systems: those where the interaction potential decays slowly for large inter-particle distances; in particular, systems where the decay is slower than the inverse inter-particle distance raised to the dimension of the embedding space. Gravitational and Coulomb interactions are the most prominent examples, however it has become clear that long-range interactions are more common than previously thought.A satisfactory understanding of properties, generally considered as oddities only a couple of decades ago, has now been reached: ensemble inequivalence, negative specific heat, negative susceptibility, ergodicity breaking, out-of-equilibrium quasi-stationary-states, anomalous diffusion. The book, intended for Master and PhD students, tries to gradually acquaint the reader with the subject. The first two parts describe the theoretical and computational instruments needed to address the study of both equilibrium and dynamical properties of systems subject to long-range forces. The third part of the book is devoted to applications of such techniques to the most relevant examples of long-range systems.PART I: STATIC AND EQUILIBRIUM PROPERTIES1. Basics of statistical mechanics of short-range interacting systems2. Equilibriumstatistical mechanics of long-range interactions3. The large deviations method and its applications4. Solutions of mean field models5. Beyond mean-field models6. Quantum long-range systemsPART II: DYNAMICAL PROPERTIES7. BBGKY hierarchy, kinetic theories and the Boltzmann equation8. Kinetic theory of long-range systems: Klimontovló#