Summer School in Les Houches (France), 4-29 August 2008
Organizers: Thierry Dauxois (ENS Lyon), Stefano Ruffo (Firenze University) and Leticia Cugliandolo (Université Paris VI and IUF)

Long-Range Interacting Systems


Statistical physics
1. Equilibrium: D. Mukamel (Israel). 6 Lectures.
2. Non-Equilibrium: J. Kurchan (France). 6 Lectures.
3. Transport: D. Dubin (USA). 6 Lectures.

Mathematical aspects
1. Equilibrium tools (Large deviations) : R. S. Ellis (USA). 3 Lectures.
2. Kinetic theory: F. Castella (France). 3 Lectures.

Self-gravitating systems: T. Padmanabhan (India). 4 Lectures.
Fluid mechanics (2D, stratified or rotating fluids): B. Turkington (USA). 4 Lectures.
Wave-particles interactions: D. Escande (France). 4 Lectures.
Dipolar effects in condensed matter: S. Bramwell (UK). 4 Lectures.
Synchronization in systems with long-range interactions : A. Pikovsky (Germany). 4 Lectures.

The school is organized around a core set of basic lectures which, starting from master level concepts, open a window over the difficulties encountered when treating long-range interactions.
Additional seminars will be given by: B. Barbara (France), P. Courteille (Germany), B. Dubrulle (France), P. Gaspard (Belgium), P. E. Jabin (France), M. Kastner (Germany), M.K.-H. Kiessling (USA), G. Robb (Scotland), W. C. Saslaw (USA).


The aim of the summer school is to present the recent development of coherent and comprehensive approaches to the theoretical and experimental study of long-range interacting systems, by integrating different disciplines and gathering together a number of leading scientists in the relevant fields. Scientists working in different fields like: astrophysics/cosmology, plasmas, 2D hydrodynamics, Coulomb interactions, theoretical statistical mechanics, will have a unique opportunity to present and discuss the common and closely related problems faced by all of them when dealing with long-range interactions.

The defining scientific focus of the school is the common need of understanding the thermodynamics and out-of-equilibrium dynamics of Long-range interacting systems. It was in the context of astrophysics that it was first appreciated, over forty years ago, that equilibrium statistical mechanics applied to Long-range interacting systems leads to some very peculiar features and problems, like negative specific heat. Insight into the self-organizing behaviour of these systems can be gained by the study of two-dimensional hydrodynamics: large-scale vortices interact via a long-range logarithmic potential (the two-dimensional analogue of the gravitational potential) and spontaneously organize into large-scale structures emerging out of a random vorticity distribution. Plasma physics (including also wave-particles physics and charged particle beams) is also a field where important advances are registered.

In recent years, primarily through the study of various simplified toy models, it has been shown that statistical physics of Long-range interacting systems generally exhibit a whole set of new qualitative properties and behaviours: ensemble inequivalence (negative specific heat, temperature jumps), long-time relaxation (quasi-stationary states), violations of ergodicity and disconnection of the energy surface, subtleties in the relation of the fluid (i.e. continuum) picture and the particle ("granular") picture, new macroscopic quantum effects, etc. Some mathematical tools (large deviations, kinetic theory) are of particular interest and dedicated lectures will be necessary. A lecture and some seminars will also concentrate on condensed matter physics. Trapped cold ions are an interesting example of mesoscopic systems, due to the possibility of manipulating their size and dimensionality through the trapping potential. These systems exhibit non-extensive properties typical of long-range interactions. Magnetic systems is another example. Usually in these systems, long range dipolar interactions are negligibly small as compared with short range exchange interactions. However, recent experiments on a quasi-one-dimensional class of compounds show that in these systems the dipolar and the exchange interactions are of the same order.

The school will provide a background for the future development of a new community, capable of fully addressing the scientific problems common to all the fields mentioned above. It can do so primarily by providing researchers in all these fields, beginning from the earliest stages of their career, with an interdisciplinary training which will expose them to the problems of Long-range interacting systems in a broader context.

Les Houches is a resort village in the Chamonix valley in the French Alps. Established in 1951, the Physics School is located in a group of chalets surrounded by meadows and woods, at an altitude of 1150 m facing the Mont-Blanc range - a very favourable environment for intellectual activity in ideal surroundings for hiking, mountaineering and sight-seeing.

The Physics School is affiliated with Université Joseph Fourier and Institut National Polytechnique de Grenoble, and is supported by the Ministère de l'Education Nationale, de l'Enseignement Supérieur et de la Recherche, by the Centre National de la Recherche Scientifique (CNRS) and by the Direction des Sciences de la Matièe du Commissariat à l'Energie Atomique (CEA/DSM).