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Statistical physics establishes a bridge from the macroscopic world to study the microscopic world. This is a theory with the fewest assumptions and the broadest conclusions. Up to now there is no evidence to show that statistical physics itself is responsible for any mistakes. Statistical physics has become an important branch of modern theoretical physics and this course has become one of the common fundamental courses of graduate students in different majors in physics departments.Statistical physics is a branch of science engaged in studying the laws of thermal motion of macroscopic systems. The advanced statistics for graduate students mainly studies quantum statistics. The first four chapters of this book are fundamental, and should be well known. The last five chapters are recent developments, including the studies on Bose-Einstein condensation, a class of inverse problems in quantum statistics (their Chen's exact solution formulas, Dai's exact solution formulas,asymptotic behavior control theory, and concrete realizations of the inversion theories), an introduction to the theory of Green's functions in quantum statistics, the unified diagonalization theorem for Hamiltonians of quadratic form, and an introduction to the third formulation of quantum statistics and the functional integral approach. This course was edited by revising the lecture notes of the author, from courses of quantum statistics and advanced statistics for graduate students,since 1978. At the same time, this work contains the research results of some related projects, supported by the National Natural Science Foundation of China.

戴顯熹：1938年5月生於溫州。1961年7月畢業於復旦大學物理係。1985年起任復旦大學物理係教授，1986年起任博士生導師。長期從事量産統計和理論物理方法研究，發錶學術論文100多篇。

自1978年以來，從事研究生的量子統計與高等統計課程教學，以及本科生的電動力學、量子力學、數理方法、超導物理、理論物理方法等課程的教學。曾獲得楊振寜教授授予的Glorious Sun奬金，曾以物理學中奇性問題研究獲教育部授予的科學進步奬(二等)等。1980年來應邀訪問過美國的休斯頓大學、紐約州立大學理論物理(楊振寜)研究所、德剋薩斯超導中心、楊伯翰大學等，曾任楊伯翰大學客座教授。在量子統計、物理學中奇性問題、一些逆問題的嚴格解及其統一理論和漸近行為控製理論等方麵作過較為係統的研究，首次由一材料的比熱實際數據中反演齣聲子譜。

Chapter 1 Fundamental Principles 1.1 Introduction: The Characters of Thermodynamics and Statistical Physics and Their Relationship 1.2 Basic Thermodynamic Identities 1.3 Fundamental Principles and Conclusions of Classical Statistics 1.3.1 Microscopic and Macroscopic Descriptions, Statistical Distribution Functions 1.3.2 Liouville Theorem 1.3.3 Statistical Independence 1.3.4 Microscopical Canonical, Canonical and Grand Canonical Ensembles 1.4 Boltzmann Gas 1.5 Density Matrix 1.5.1 Density Matrix 1.5.2 Some General Properties of the Density Matrix 1.6 Liouville Theorem in Quantum Statistics 1.7 Canonical Ensemble 1.8 Grand Canonical Ensemble 1.8.1 Fundamental Expression of the Grand Canonical Ensemble 1.8.2 Derivation of the Fundamental Thermodynamic Identity 1.9 Probability Distribution and Slater Sum 1.9.1 Meaning of the Diagonal Elements of the Density Matrix 1.9.2 Slater Summation 1.9.3 Example : Probability of the Harmonic Ensemble 1.10 Theory of the Reduced Density MatrixChapter 2 The Perfect Gas in Quantum Statistics 2.1 Indistinguishability Principle for Identical Particles 2.2 Bose Distribution and Fermi Distribution 2.2.1 Perfect Gases in Quantum Statistics 2.2.2 Bose Distribution 2.2.3 Fermi Distribution 2.2.4 Comparison of Three Distributions;Gibbs Paradox Again ……Chapter 3 Second Quantization and Model HamiltoniansChapter 4 Least Action Principle, Field Quantization and the Electron-Phonon SystemChapter 5 Bose-Einstein CondensationChapter 6 Some Inverse Problems in Quanturn StatistiesChapter 7 An Introduction to Theory of Green's FunctionsChapter 8 A Unified Diagonalization Theorem for Quadratic HamiltonianChapter 9 Functional Integral Approach: A Third Formulation of Quantum Statistical MechanicsReferencesIndex
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