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Full Description
A study of the equilibrium properties of Coulomb systems in physics that is the first of its kind.
This book studies the equilibrium properties of Coulomb systems, namely classical or quantum systems of charged particles interacting purely with the Coulomb force, drawing on results that are mathematically rigorous or derived from formal perturbation series, without resorting to ad hoc modeling or phenomenological descriptions. It also includes the findings of ab initio numerical simulations, as well as a presentation of simple and accurate approximations. Exercises with corrections are proposed
There are two main themes. The first aims to gather and summarize the demonstrations of fundamental theorems on the stability and extensivity of matter, the screening phenomena, and the existence of atomic and molecular phases. The second theme revolves around an in-depth analysis of the Coulombic correlations by means of diagrammatic series of Mayer type, that incorporate screening in a non perturbative way. This tool is well suited to low-density calculations of van der Waals forces and viral expansions in fully or partially ionized regimes. Considerations about the Kosterlitz-Thouless transition and phase transitions in simple models are also presented. The book is the first of its kind, providing an authoritative text for any physicist working in this area.
Contents
Contents
Introduction
1 From Macroscopic Electrostatics to Microscopic Screening
2 Screening Within Linear Response Theory
3 Charge and Field Fluctuations
4 Statistical Mechanical Models
5 Stability and Extensivity in the Thermodynamic Limit
6 Screened Mayer Expansions
7 Diagrammatic Analysis of Exponential Screening
8 Classical Correlations: Non-Perturbation Results
9 Solvable Models and Numerical Simulations
10 Breakdown of Debye Screening for Quantum Charges
11 The Gas of Loops and the Quantum Analog of the Debye Potential
12 The Low-Density Weakly Degenerate Regime
13 Grand Canonical Diagrammatic Representation
14 Quantum Correlations at Large Distances
15 Atoms and Molecules
16 Van der Waals Forces
17 Thermodynamic Relations and Classical Equations of State
18 Quantum Thermodynamic Functions
19 The Kosterlitz-Thouless Transition
20 Phase Transitions in Simple Systems
Appendices
A Linear Response Theory - B Statistical Independence and Clustering - C Gaussian Integrals and Gaussian Fields - D Mayer Diagrams - E The Sine-Gordon Representation - F The YBG Hierarchy for Coulomb Systems - G The Feynman-Kac Representation - H Statistical Mechanics of Loops - I Density Functional Theory
Notations repertory
Acknowledgments
