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.

PART 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

A. Campa is Senior Scientist at the Health and Technology Department of the Istituto Superiore di Sanità, Roma (Italy). He holds a Laurea in Physics (University of Roma "La Sapienza") and a Ph.D. in Physics (The Rockefeller University, New York, USA). His activities are in statistical physics, nonlinear dynamics, radiation physics, and modelling of ionizing radiation effects on biological systems. He worked as a postdoc of the Italian National Institute of the Physics of Matter (INFM) and he is now associated to the Italian National Institute of Nuclear Physics (INFN). T. Dauxois is a CNRS Research Director at the Ecole Normale Supérieure de Lyon (France). His scientific activity is in nonlinear physics and statistical physics, with applications to condensed matter and hydrodynamics. He was the Head of Graduate Studies in Physics (M2) at ENS-Lyon (2005-11), Chairman of the Committee for Theoretical Physics in CNRS (2010-12) and is now Director of the Physics Laboratory at ENS de Lyon. D. Fanelli is Associate Professor in the Department of Physics and Astronomy at the University of Florence (Italy). Fanelli's research interests fall in the realm of statistical mechanics and nonlinear physics, with applications to biology and biophysics. He holds a Laurea in Physics (University of Florence) and a Ph.D. In Numerical Analysis and Computer Science (KTH, Stockholm). He worked as a postdoc and researcher at the Karolinska Institute in Stockholm and as permanent staff member (Lecturer in Theoretical Physics) at the University of Manchester. He was also awarded the prestigious "Rientro dei Cervelli" grant. S. Ruffo is a Full Professor in the Department of Physics and Astronomy of the University of Florence (Italy). His scientific activity is in the field of statistical and nonlinear physics. He is an editor of 'Communications in Nonlinear Science and Numerical Simulations'. He has been Weston Visiting Professor at The Weizmann Institute of Science, Department of Physics of