Dynamics and Thermodynamics of Systems with Long-Range Interactions

Thierry Dauxois, Stefano Ruffo, Ennio Arimondo, Martin Wilkens (auth.), Thierry Dauxois, Stefano Ruffo, Ennio Arimondo, Martin Wilkens (eds.)3540443150, 9783540443155

Properties of systems with long range interactions are still poorly understood despite being of importance in most areas of physics. The present volume introduces and reviews the effort of constructing a coherent thermodynamic treatment of such systems by combining tools from statistical mechanics with concepts and methods from dynamical systems. Analogies and differences between various systems are examined by considering a large range of applications, with emphasis on Bose–Einstein condensates. Written as a set of tutorial reviews, the book will be useful for both the experienced researcher as well as the nonexpert scientist or postgraduate student.

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Table of contents :
Dynamics and Thermodynamics of Systems with Long-Range Interactions: An Introduction….Pages 1-19
Thermo-statistics or Topology of the Microcanonical Entropy Surface….Pages 23-44
Ensemble Inequivalence in Mean-Field Models of Magnetism….Pages 45-67
Phase Transitions in Finite Systems….Pages 68-129
Phase Transitions in Systems with 1/ r α Attractive Interactions….Pages 130-139
Nonextensivity: From Low-Dimensional Maps to Hamiltonian Systems….Pages 140-162
Statistical Mechanics of Gravitating Systems in Static and Cosmological Backgrounds….Pages 165-207
Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems….Pages 208-289
Coherence and Superfluidity of Gaseous Bose-Einstein Condensates….Pages 293-311
Ultracold Atoms and Bose-Einstein Condensates in Optical Lattices….Pages 312-331
Canonical Statistics of Occupation Numbers for Ideal and Weakly Interacting Bose-Einstein Condensates….Pages 332-368
New Regimes in Cold Gases via Laser-Induced Long-Range Interactions….Pages 369-403
Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model….Pages 407-436
Kinetic Theory for Plasmas and Wave-Particle Hamiltonian Dynamics….Pages 437-447
Emergence of Fractal Clusters in Sequential Adsorption Processes….Pages 448-457
The Hamiltonian Mean Field Model: From Dynamics to Statistical Mechanics and Back….Pages 458-487