Applications Of Field Theory Methods In Statistical Physics Of Nonequilibrium Systems

✍ Scribed by Bohdan I Lev, Anatoly G Zagorodny

• Publisher: World Scientific
• Year: 2021
• Tongue: English
• Leaves: 352
• Category: Library

✦ Synopsis

This book formulates a unified approach to the description of many-particle systems combining the methods of statistical physics and quantum field theory. The benefits of such an approach are in the description of phase transitions during the formation of new spatially inhomogeneous phases, as well in describing quasi-equilibrium systems with spatially inhomogeneous particle distributions (for example, self-gravitating systems) and metastable states.The validity of the methods used in the statistical description of many-particle systems and models (theory of phase transitions included) is discussed and compared. The idea of using the quantum field theory approach and related topics (path integration, saddle-point and stationary-phase methods, Hubbard-Stratonovich transformation, mean-field theory, and functional integrals) is described in detail to facilitate further understanding and explore more applications.To some extent, the book could be treated as a brief encyclopedia of methods applicable to the statistical description of spatially inhomogeneous equilibrium and metastable particle distributions. Additionally, the general approach is not only formulated, but also applied to solve various practically important problems (gravitating gas, Coulomb-like systems, dusty plasmas, thermodynamics of cellular structures, non-uniform dynamics of gravitating systems, etc.).

✦ Table of Contents

Contents
Preface
Introduction
1. Statistical Physics of Interacting Particle Systems
1.1 Systems of Particles with Interaction
1.2 Models of Statistical Physics
1.3 The Model of Hard Spheres with Attractive Interaction
1.4 Nonideal Gas at Low Temperatures
2. Statistical Description of Phase Transitions
2.1 Theory of the Second-Order Phase Transitions Bragg–Williams theory
2.2 Unification of the Theories of Phase Transitions
2.3 First-Order Phase Transitions
2.4 Dynamics of Metastable States
3. Path Integration and Field Theory
3.1 Classical and Quantum Systems
3.2 Saddle-Point Method or Stationary-Phase Method
3.3 Construction of the Field Theory
3.4 Hubbard–Stratonovich Transformation
3.5 The Mean-Field Theory and the Functional Integral
4. Peculiarity of Calculation of Some Models
4.1 Special Cases of the Calculation of Path Integrals
4.2 Harmonic Lattice Model
4.3 The n-Vector Model
4.4 Potts Model
4.5 Villain and Gauss Lattice Models
4.6 Two-Dimensional Coulomb-Gas Models
5. Statistical Description of Condensed Matter
5.1 Partition Function for Model Systems
5.2 Ideal Classical and Quantum Gases
5.3 Hard Spheres Model
5.4 Two Exactly Solvable Models of Statistical Physics
5.5 Gravitating Gas Model
5.6 Coulomb-like Systems
6. Inhomogeneous Distribution in Systems of Particles
6.1 Microcanonical Description of Gravitating Systems
6.2 Spatial Distribution Function
6.3 Inhomogeneity of Self-Gravitating Systems Statistical approach
6.4 Conditions for the Gravothermal Catastrophe Infinite system
6.5 Models with Attraction and Repulsion
7. Cellular Structures in Condensed Matter
7.1 Cellular Structures and Selection of States
7.2 Thermodynamic of Cellular Structures
7.3 Cellular Structures in Colloids
7.4 Geometry of the Distribution of Interacting Particles
8. Statistical Description of Nonequilibrium Systems
8.1 Nonequilibrium Gravitating Systems
8.2 Systems with Repulsive Interaction
8.3 Saddle States of Nonequilibrium Systems
8.4 Nonequilibrium Dynamics of Universe Formation
Conclusions
Bibliography
Index