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A Kinetic View of Statistical Physics

Book Description

Aimed at graduate students, this book explores some of the core phenomena in non-equilibrium statistical physics. It focuses on the development and application of theoretical methods to help students develop their problem-solving skills. The book begins with microscopic transport processes: diffusion, collision-driven phenomena, and exclusion. It then presents the kinetics of aggregation, fragmentation and adsorption, where the basic phenomenology and solution techniques are emphasized. The following chapters cover kinetic spin systems, both from a discrete and a continuum perspective, the role of disorder in non-equilibrium processes, hysteresis from the non-equilibrium perspective, the kinetics of chemical reactions, and the properties of complex networks. The book contains 200 exercises to test students' understanding of the subject. A link to a website hosted by the authors, containing supplementary material including solutions to some of the exercises, can be found at www.cambridge.org/9780521851039.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. Preface
  7. Conventions
  8. 1. Aperitifs
    1. 1.1 Diffusion
    2. 1.2 Single-species annihilation/coalescence
    3. 1.3 Two-species annihilation
    4. 1.4 Notes
  9. 2. Diffusion
    1. 2.1 The probability distribution
    2. 2.2 Central limit theorem
    3. 2.3 Walks with broad distributions
    4. 2.4 Application to gravity: the Holtsmark distribution
    5. 2.5 First-passage properties
    6. 2.6 Exit probabilities and exit times
    7. 2.7 Reaction rate theory
    8. 2.8 The Langevin approach
    9. 2.9 Application to surface growth
    10. 2.10 Notes
    11. 2.11 Problems
  10. 3. Collisions
    1. 3.1 Kinetic theory
    2. 3.2 The Lorentz gas
    3. 3.3 Lorentz gas in an external field
    4. 3.4 Collisional impact
    5. 3.5 Maxwell molecules and very hard particles
    6. 3.6 Inelastic gases
    7. 3.7 Ballistic agglomeration
    8. 3.8 Single-lane traffic
    9. 3.9 Notes
    10. 3.10 Problems
  11. 4. Exclusion
    1. 4.1 Symmetric exclusion process
    2. 4.2 Asymmetric exclusion process
    3. 4.3 Hydrodynamic approach
    4. 4.4 Microscopic approach
    5. 4.5 Open systems
    6. 4.6 Notes
    7. 4.7 Problems
  12. 5. Aggregation
    1. 5.1 The master equations
    2. 5.2 Exact solution methods
    3. 5.3 Gelation
    4. 5.4 Scaling
    5. 5.5 Aggregation with input
    6. 5.6 Exchange-driven growth
    7. 5.7 Notes
    8. 5.8 Problems
  13. 6. Fragmentation
    1. 6.1 Binary fragmentation
    2. 6.2 Planar fragmentation
    3. 6.3 Reversible polymerization
    4. 6.4 Collisional fragmentation
    5. 6.5 Notes
    6. 6.6 Problems
  14. 7. Adsorption
    1. 7.1 Random sequential adsorption in one dimension
    2. 7.2 Phase space structure
    3. 7.3 Adsorption in higher dimensions
    4. 7.4 Reversible adsorption
    5. 7.5 Polymer translocation
    6. 7.6 Notes
    7. 7.7 Problems
  15. 8. Spin dynamics
    1. 8.1 Phenomenology of coarsening
    2. 8.2 The voter model
    3. 8.3 Ising–Glauber model
    4. 8.4 Mean-field approximation
    5. 8.5 Glauber dynamics in one dimension
    6. 8.6 Glauber dynamics in higher dimensions
    7. 8.7 Spin-exchange dynamics
    8. 8.8 Cluster dynamics
    9. 8.9 Notes
    10. 8.10 Problems
  16. 9. Coarsening
    1. 9.1 Models
    2. 9.2 Free evolution
    3. 9.3 Case studies in non-conservative dynamics
    4. 9.4 Final states
    5. 9.5 Defects
    6. 9.6 Conservative dynamics
    7. 9.7 Extremal dynamics
    8. 9.8 Nucleation and growth
    9. 9.9 Notes
    10. 9.10 Problems
  17. 10. Disorder
    1. 10.1 Disordered spin chain
    2. 10.2 Random walk in a random potential
    3. 10.3 Random walk in random velocity fields
    4. 10.4 Notes
    5. 10.5 Problems
  18. 11. Hysteresis
    1. 11.1 Homogeneous ferromagnets
    2. 11.2 Perturbation analysis
    3. 11.3 Disordered ferromagnets
    4. 11.4 Mean-field model
    5. 11.5 Hysteresis in the random-field Ising chain
    6. 11.6 Notes
    7. 11.7 Problems
  19. 12. Population dynamics
    1. 12.1 Continuum formulation
    2. 12.2 Discrete reactions
    3. 12.3 Small-fluctuation expansion
    4. 12.4 Large fluctuations
    5. 12.5 Notes
    6. 12.6 Problems
  20. 13. Diffusive reactions
    1. 13.1 Role of the spatial dimension
    2. 13.2 The trapping reaction
    3. 13.3 Two-species annihilation
    4. 13.4 Single-species reactions in one dimension
    5. 13.5 Reactions in spatial gradients
    6. 13.6 Notes
    7. 13.7 Problems
  21. 14. Complex networks
    1. 14.1 Non-lattice networks
    2. 14.2 Evolving random graphs
    3. 14.3 Random recursive trees
    4. 14.4 Preferential attachment
    5. 14.5 Fluctuations in networks
    6. 14.6 Notes
    7. 14.7 Problems
  22. References
  23. Index