Long-Range Interacting Systems Lecture Notes of the Les Houches Summer School: Volume 90, August 2008 Lecture Notes of the Les Houches Summer School Series

This book collects together the lecture courses and seminars given at the Les Houches Summer School 2008 on Long-Range Interacting Systems. Leading scientists in different fields of mathematics and physics present their views on this fast growing and interdisciplinary field of research, by venturing upon fundamental problems of probability, transport theory, equilibrium and non-equilibrium statistical mechanics, condensed matter physics, astrophysics and cosmology, physics of plasmas, and hydrodynamics. The thermodynamic and dynamical properties of systems with long-range interactions were poorly understood until a few years ago. Substantial progress has been made only recently by realizing that the lack of additivity induced by long-range interactions does not hinder the development of a consistent thermodynamic formalism. This book reviews the state-of-the-art developments in this field and provides an essential background to future studies. All chapters are written from a pedagogical perspective, making the book accessible to masters and PhD students and all researchers wishing to enter this field.

Part I: STATISTICAL DYNAMICS. 1. Statistical Mechanics of Systems with Long-Range Interactions. 2. Six out of equilibrium lectures. 3. Synchronization of regular and chaotic oscillators. Part II: HYDRODYNAMICS. 4. Statistical Mechanics of Two-dimensional and Quasi-geostrophic Flows. 5. Statistical Mechanics of Turbulent Von Karman Flows: Theory and Experiments. Part III: MATHEMATICAL ASPECTS. 6. The Theory of Large Deviations and Applications to Statistical Mechanics. 7. Solving Ordinary Differential Equations when the coefficients have low regularity : a kinetic point of view (after R. Di Perna and P.L. Lions). 8. Mean Field Limit for Interacting Particles. 9. On the Origin of Phase Transitions in Long- and Short-range Interacting Systems. Part IV: GRAVITATIONAL INTERACTION. 10. Statistical Mechanics of Gravitating Systems: an Overview. 11. Statistical Mechanics of the Cosmological Many-body Problem and its Relation to Galaxy Clustering. 12. A Lecture on the Relativistic Vlasov-Poisson Equations. Part V: COULOMB ABD WAVE-PARTICLE INTERACTION. 13. Plasma Collisional Transport. 14. Wave-particle interaction in plasmas: a qualitative approach. 15. Long-Range Interaction in Cold Atom Optics. 16. Collective Instabilities in Light-Matter Interactions. Part VI: DIPOLAR INTERACTION IN CONDENSED MATTER. 17. Dipolar Effects in Condensed Matter.

Prof. Leticia F. Cugliandolo, born in 1965, got her PhD in Physics from Universidad Nacional de La Plata, Argentina, in 1991. Subsequently, she spent a three year post-doc at Università di Roma I, La Sapienza, and then moved to the Service de Physique de l'Etat Condensé at Saclay (CEA) and Ecole Normale Supérieure (ENS) de Paris for a second post-doctoral experience. In 1997 she became assistant professor at ENS Paris and in 2003 full professor at Université Pierre et Marie Curie - Paris VI where she presently teaches and pursues her research acivities. Since January 2007 she has been the Director of the Ecole de Physique des Houches. Dr. Thierry Dauxois took his PhD in 1993 from Dijon University (France) in collaboration with Los Alamos National Laboratory. In 1994, he became CNRS researcher at Ecole Normale Supérieure in Lyon. He got a Marie Curie fellowship in 1996 to spend 6 months at Firenze University and a NATO fellowship in 1997 to spend one year at the Scripps Institution of Oceanography, University of California San Diego. His main field of research is nonlinear physics and statistical mechanics, with applications to biophysics, condensed matter and hydrodynamics. Prof. Stefano Ruffo, born in 1954, got his Laurea in Physics from Florence University (Italy) in 1977. In 1987 he won a national competition for an Associate Professorship in Condensed Matter Physics at the University of Basilicata. He moved to the Faculty of Engineering, University of Florence, in 1991, where presently he teaches basic physics and dynamical systems. He is a member of the Advisory Board of Physica A (Elsevier) and an Editor of Communications in Nonlinear Science and Numerical Simulations (Elsevier). He has recently become a member of the C3 Commission (Statistical Physics) of the IUPAP.

The lecturers and authors of the chapters form an impressive list, all being leading scientists in the respective fields. [] This book provides, in a style accessible to graduate and PhD students, the necessary background about what has been achieved so far and what is likely to come in the near future. I believe this volume will remain for long an essential textbook and a reference to young researchers wishing to enter this expanding research field.