Statistical Mechanics of Coulomb Systems

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, i.e. classical or quantum systems of charged particles interacting exclusively with the Coulomb force, drawing on results that are mathematically rigorous or derived from formal perturbation series, without ad hoc modeling or intermediate approximations. Two main themes form the essential purpose of Statistical Mechanics of Coulomb Systems: the simplified description of the proofs of four fundamental theorems on the existence of Coulomb matter on the one hand and the development of a formalism based on diagrammatic expansions adapted to the treatment of classical and quantum screening phenomena on the other hand. The result is an authoritative analysis of Coulomb systems that will be essential for any physicist working in this area.  

Table of 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

About the Author :
A native of Geneva, Philippe-André Martin studied physics at the University of Geneva. Angel Alastuey is a theoretical physicist. He was director of research at the Physics Laboratory of the ENS Lyon.