Statistical Mechanics 2nd Edition by Franz Schwabl

• Basic Principles
• Equilibrium Ensembles
• Thermodynamics
• Ideal Quantum Gases
• Real Gases, Liquids, and Solutions
• Magnetism
• Phase Transitions, Renormalization Group Theory, and Percolation
• Brownian Motion, Equations of Motion and the Fokker–Planck Equations
• The Boltzmann Equation
• Irreversibility and the Approach to Equilibrium

Preface to Statistical Mechanics Second Edition PDF

In this new edition, supplements, additional explanations, and cross-references have been added in numerous places, including additional problems and revised formulations of the problems. Figures have been redrawn and the layout improved.

In all these additions I have pursued the goal of not changing the compact character of the book. I wish to thank Prof. W. Brewer for integrating these changes into his competent translation of the first edition.

I am grateful to all the colleagues and students who have made suggestions to improve the book as well as to the publisher, Dr. Thorsten Schneider and Mrs. J. Lenz for their excellent cooperation.

Preface to the Statistical Mechanics First Edition

This book deals with statistical mechanics. Its goal is to give a deductive presentation of the statistical mechanics of equilibrium systems based on a single hypothesis – the form of the microcanonical density matrix – as well as to treat the most important aspects of non-equilibrium phenomena.

Beyond the fundamentals, the attempt is made here to demonstrate the breadth and variety of the applications of statistical mechanics.

Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications in critical dynamics are treated.

A compact presentation was preferred wherever possible; it, however, requires no additional aids except for knowledge of quantum mechanics. The material is made as understandable as possible by the inclusion of all the mathematical steps and a complete and detailed presentation of all intermediate calculations.

At the end of each chapter, a series of problems is provided. Subsections that can be skipped over in a first reading are marked with an asterisk; subsidiary calculations and remarks that are not essential for comprehending the material are shown in small print.

Where it seems helpful, literature citations are given; these are by no means complete but should be seen as an incentive to further reading.

A list of relevant textbooks is given at the end of each of the more advanced chapters. The first chapter presents the fundamental concepts of probability theory and the properties of distribution functions and density matrices.

In Chapter 2, the microcanonical ensemble and, building upon it, basic quantities such as entropy, pressure, and temperature are introduced. Following this, the density matrices for the canonical and the grand canonical ensemble are derived.

The third chapter is devoted to thermodynamics. Here, the usual material (thermodynamic potentials, the laws of thermodynamics, cyclic processes, etc.) are treated, with special attention given to the theory of phase transitions, to mixtures and to border areas related to physical chemistry.

Chapter 4 deals with the statistical mechanics of ideal quantum systems, including the Bose-Einstein condensation, the radiation field, and superfluids.

In Chapter 5, real gases and liquids are treated (internal degrees of freedom, the van der Waals equation, mixtures). Chapter 6 is devoted to the subject of magnetism, including magnetic phase transitions.

Furthermore, related phenomena such as the elasticity of rubber are presented. Chapter 7 deals with the theory of phase transitions and critical phenomena; following a general overview, the fundamentals of renormalization group theory are given.

In addition, the Ginzburg–Landau theory is introduced, and percolation is discussed (as a topic related to critical phenomena).

The remaining three chapters deal with non-equilibrium processes: Brownian motion, the Langevin and Fokker–Planck equations and their applications as well as the theory of the Boltzmann equation and from it, the H-Theorem and hydrodynamic equations.

In the final chapter, dealing with the topic of irreversibility, fundamental considerations of how it occurs, and of the transition to equilibrium are developed.

In appendices, among other topics, the Third Law and a derivation of the classical distribution function starting from quantum statistics are presented, along with the microscopic derivation of the hydrodynamic equations.

The book is recommended for students of physics and related areas from the 5th or 6th semesters on. Parts of it may also be of use to teachers.

It is suggested that students at first skip over the sections marked with asterisks or shown in small print, and thereby concentrate their attention on the essential core material.

This book evolved out of lecture courses given numerous times by the author at the Johannes Kepler Universit¨at in Linz (Austria) and at the Technische Universit¨at in Munich (Germany).

Many coworkers have contributed to the production and correction of the manuscript: I. Wefers, E. J¨org-M¨uller, M. Hummel, A. Vilfan, J. Wilhelm, K. Schenk, S. Clar, P. Maier, B. Kaufmann, M. Bulenda, H. Schinz, and A. Won has. W. Gasser read the whole manuscript several times and made suggestions for corrections.

Advice and suggestions from my former coworkers E. Frey and U. C. T¨auber were likewise quite valuable.

I wish to thank Prof. W. D. Brewer for his faithful text translation. I want to express my sincere gratitude to all of them, along with those of my other associates who offered valuable assistance, as well as to Dr. H. J. K¨olsch, representing the Springer-Verlag.

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Author(s): Franz Schwabl, William D. Brewer

Series: Springer-Lehrbuch

Publisher: Springer, Year: 2010

ISBN: 3642068871,9783642068874

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