Dynamics and Thermodynamics of Systems With Long Range Interactions

by Dauxois, T.; Ruffo, S.; Arimondo, E.; Wilkens, Martin

• ISBN13: 9783540443155
• ISBN10: 3540443150
• Format: Hardcover
• Copyright: 2003-02-01
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Dynamics and Thermodynamics of Systems with Long-Range Interactions: An Introduction	p. 1
Statistical Mechanics
Thermo-statistics or Microcanonical Topology of the Microcanonical Entropy Surface	p. 23
Ensemble Inequivalence in Mean-Field Models of Magnetism	p. 45
Phase Transitions in Finite Systems	p. 68
Phase Transitions in Systems with 1/r[superscript [alpha]] Attractive Interactions	p. 130
Nonextensivity: From Low-Dimensional Maps to Hamiltonian Systems	p. 140
Astrophysics
Statistical Mechanics of Gravitating Systems in Static and Cosmological Backgrounds	p. 165
Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems	p. 208
Bose-Einstein Condensation
Coherence and Superfluidity of Gaseous Bose-Einstein Condensates	p. 293
Ultracold Atoms and Bose-Einstein Condensates in Optical Lattices	p. 312
Canonical Statistics of Occupation Numbers for Ideal and Weakly Interacting Bose-Einstein Condensates	p. 332
New Regimes in Cold Cases via Laser-Induced Long-Range Interactions	p. 369
Nonlinear Dynamics
Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model	p. 407
Kinetic Theory for Plasmas and Wave-Particle Hamiltonian Dynamics	p. 437
Emergence of Fractal Clusters in Sequential Adsorption Processes	p. 448
The Hamiltonian Mean Field Model: From Dynamics to Statistical Mechanics and Back	p. 458
Index	p. 489
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