Physics of Long-Range Interacting 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. This is a very interesting and timely book. Systems characterised by long range interactions, be they electromagnetic, gravitational or hydrodynamic, pose special problems. The authors show in a clear and systematic way how methods of statistical physics can advance understanding of both equilibrium and non equilibrium behaviour. The book, which emphasises interdisciplinary aspects and applications from several areas of physics, is well written and a pleasure to read. Peter Richmond, Trinity College Dublin An essential textbook for students and a useful tool for researchers, this timely work collects in one single volume clear and useful statistical physicist approaches to short-range systems, out-of-equilibrium dynamics, and long-range interactions. Guido Caldarelli, IMT Alti Studi LuccaPART I: STATIC AND EQUILIBRIUM PROPERTIES ; 1. Basics of statistical mechanics of short-range interacting systems ; 2. Equilibriumstatistical mechanics of long-range interactions ; 3. The large deviations method and its applications ; 4. Solutions of mean field models ; 5. Beyond mean-field models ; 6. Quantum long-range systems ; PART II: DYNAMICAL PROPERTIES ; 7. BBGKY hierarchy, kinetic theories and the Boltzmann equation ; 8. Kinetic theory of long-range systems: Klimontovich, Vlasov and Lenard-Balescu equations ; 9. Out-of-equilibrium dynamics and slow relaxation ; PART III: APPLICATIONS ; 10. Gravitational systems ; 11. Two-dimensional and geophysical fluid mechanics ; 12. Cold Coulomb systems ; 13. Hot plasma ; 14. Wave-particles interaction ; 15. Dipolar systems ; Appendix A: Features of the main models studied throughout the book ; Appendix B: Evaluation of the Laplace integral outside the analyticity strip ; Appendix C: The equilibrium form of the one-particle distribution function in short-range interacting systems ; Appendix D: The differential cross section of a binary collision ; Appendix E: Autocorrelation of the fluctuations of the one-particle density ; Appendix F: Derivation of the Fokker-Planck coefficients