A. Campa
Physics of long-range interacting systems - 1st Ed. - Oxford, U.K. Oxford University Press 2014 - xvi, 410 p.
PART I: STATIC AND EQUILIBRIUM PROPERTIES
1. Basics of statistical mechanics of short-range interacting systems
2. Equilibriumstatistical mechanics of long-range interactions
3. The large deviations method and its applications
4. Solutions of mean field models
5. Beyond mean-field models
6. Quantum long-range systems
PART II: DYNAMICAL PROPERTIES
7. BBGKY hierarchy, kinetic theories and the Boltzmann equation
8. Kinetic theory of long-range systems: Klimontovich, Vlasov and Lenard-Balescu equations
9. Out-of-equilibrium dynamics and slow relaxation
PART III: APPLICATIONS
10. Gravitational systems
11. Two-dimensional and geophysical fluid mechanics
12. Cold Coulomb systems
13. Hot plasma
14. Wave-particles interaction
15. Dipolar systems
Appendix A: Features of the main models studied throughout the book
Appendix B: Evaluation of the Laplace integral outside the analyticity strip
Appendix C: The equilibrium form of the one-particle distribution function in short-range interacting systems
Appendix D: The differential cross section of a binary collision
Appendix E: Autocorrelation of the fluctuations of the one-particle density
Appendix F: Derivation of the Fokker-Planck coefficients.
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 part of the book is devoted to applications of such techniques to the most relevant examples of long-range systems.
(source: Nielsen Book Data; retrieved from Stanford libraries catalog)
9780199581931
Statistical physics
System theory
QC174.84
Physics of long-range interacting systems - 1st Ed. - Oxford, U.K. Oxford University Press 2014 - xvi, 410 p.
PART I: STATIC AND EQUILIBRIUM PROPERTIES
1. Basics of statistical mechanics of short-range interacting systems
2. Equilibriumstatistical mechanics of long-range interactions
3. The large deviations method and its applications
4. Solutions of mean field models
5. Beyond mean-field models
6. Quantum long-range systems
PART II: DYNAMICAL PROPERTIES
7. BBGKY hierarchy, kinetic theories and the Boltzmann equation
8. Kinetic theory of long-range systems: Klimontovich, Vlasov and Lenard-Balescu equations
9. Out-of-equilibrium dynamics and slow relaxation
PART III: APPLICATIONS
10. Gravitational systems
11. Two-dimensional and geophysical fluid mechanics
12. Cold Coulomb systems
13. Hot plasma
14. Wave-particles interaction
15. Dipolar systems
Appendix A: Features of the main models studied throughout the book
Appendix B: Evaluation of the Laplace integral outside the analyticity strip
Appendix C: The equilibrium form of the one-particle distribution function in short-range interacting systems
Appendix D: The differential cross section of a binary collision
Appendix E: Autocorrelation of the fluctuations of the one-particle density
Appendix F: Derivation of the Fokker-Planck coefficients.
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 part of the book is devoted to applications of such techniques to the most relevant examples of long-range systems.
(source: Nielsen Book Data; retrieved from Stanford libraries catalog)
9780199581931
Statistical physics
System theory
QC174.84