Physics of Long-Range Interacting Systems

Synopsis

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.--cover. Basics Of Statistical Mechanics Of Short-range Interacting Systems -- Equilibrium Statistical Mechanics Of Long-range Interactions -- The Large Deviations Method And Its Applications -- Solutions Of Mean Field Models -- Beyond Mean-field Models -- Quantum Long-range Systems -- Bbgky Hierarchy, Kinetic Theories And The Boltzmann Equation -- Kinetic Theory Of Long-range Systems: Klimontovich, Vlasov And Lenard-balescu Equations -- Out-of-equilibrium Dynamics And Slow Relaxation -- Gravitational Systems -- Two-dimensional And Geophysical Fluid Mechanics -- Cold Coulomb Systems -- Hot Plasma -- Wave-particles Interaction -- Dipolar Systems -- Appendixes: A. Features Of The Main Models Studied Throughout The Book -- B. Evaluation Of The Laplace Integral Outside The Analyticity Strip -- C. The Equilibrium Form Of The One-particle Distribution Function In Short-range Interacting Systems -- D. The Differential Cross-section Of A Binary Collision -- E. Autocorrelation Of The Fluctuations Of The One-particle Density -- F. Derivation Of The Fokker-planck Coefficients. A. Campa, T. Dauxois, D. Fanelli And S. Ruffo. Includes Bibliographical References And Index.