Physics of Long-Range Interacting Systems

Hardcover | October 29, 2014

byA. Campa, T. Dauxois, D. Fanelli

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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. A satisfactory understanding of properties, generally considered as oddities only a couple of decades ago, has now been reached: ensemble inequivalence, negative specific heat, negative susceptibility, ergodicity breaking, out-of-equilibrium quasi-stationary-states, anomalous diffusion. The book,intended for Master and PhD students, tries to gradually acquaint the reader with the subject. The first two parts describe the theoretical and computational instruments needed to address the study of both equilibrium and dynamical properties of systems subject to long-range forces. The third partof the book is devoted to applications of such techniques to the most relevant examples of long-range systems.

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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 mos...

A. Campa is Senior Scientist at the Health and Technology Department of the Istituto Superiore di Sanita, Roma (Italy). He holds a Laurea in Physics (University of Roma "La Sapienza") and a Ph.D. in Physics (The Rockefeller University, New York, USA). His activities are in statistical physics, nonlinear dynamics, radiation physics, and...
Format:HardcoverDimensions:448 pages, 9.69 × 6.73 × 0.01 inPublished:October 29, 2014Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199581932

ISBN - 13:9780199581931

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Table of Contents

PART I: STATIC AND EQUILIBRIUM PROPERTIES1. Basics of statistical mechanics of short-range interacting systems2. Equilibriumstatistical mechanics of long-range interactions3. The large deviations method and its applications4. Solutions of mean field models5. Beyond mean-field models6. Quantum long-range systemsPART II: DYNAMICAL PROPERTIES7. BBGKY hierarchy, kinetic theories and the Boltzmann equation8. Kinetic theory of long-range systems: Klimontovich, Vlasov and Lenard-Balescu equations9. Out-of-equilibrium dynamics and slow relaxationPART III: APPLICATIONS10. Gravitational systems11. Two-dimensional and geophysical fluid mechanics12. Cold Coulomb systems13. Hot plasma14. Wave-particles interaction15. Dipolar systemsAppendix A: Features of the main models studied throughout the bookAppendix B: Evaluation of the Laplace integral outside the analyticity stripAppendix C: The equilibrium form of the one-particle distribution function in short-range interacting systemsAppendix D: The differential cross section of a binary collisionAppendix E: Autocorrelation of the fluctuations of the one-particle densityAppendix F: Derivation of the Fokker-Planck coefficients