高等統(tǒng)計(jì)物理

前言

　　統(tǒng)計(jì)物理架起人們由宏觀世界研究微觀世界的橋梁。凡出現(xiàn)B0ltzmann常數(shù)的理論就涉及統(tǒng)計(jì)物理。它是假設(shè)最少，結(jié)論眾多的一門(mén)學(xué)科。至今還沒(méi)有任何證據(jù)，確認(rèn)某些錯(cuò)誤必須由統(tǒng)計(jì)物理本身負(fù)責(zé)。這反映出該學(xué)科自然的關(guān)?！　∷殉蔀楝F(xiàn)代理論物理的一個(gè)重要部分。同時(shí)它又滲透到物理學(xué)的眾多領(lǐng)域，因此自然成為物理系的多個(gè)專(zhuān)業(yè)的研究生基礎(chǔ)課程?！　〗y(tǒng)計(jì)物理是研究體系的熱運(yùn)動(dòng)規(guī)律的學(xué)科。它有自己的特殊規(guī)律，不能從力學(xué)推導(dǎo)出來(lái)。但必須以力學(xué)為其基礎(chǔ)之一?；诮?jīng)典力學(xué)的，稱(chēng)經(jīng)典統(tǒng)計(jì)，基于量子力學(xué)的，稱(chēng)量子統(tǒng)計(jì)。通常大學(xué)生基礎(chǔ)課程中的統(tǒng)計(jì)物理以研究經(jīng)典統(tǒng)計(jì)為主，而研究生的高等統(tǒng)計(jì)，則以量子統(tǒng)計(jì)為主?！　”緯?shū)的第一章是統(tǒng)計(jì)物理基本原理。第二章作為這些基本原理的簡(jiǎn)單應(yīng)用，解決幾個(gè)典型的統(tǒng)計(jì)物理問(wèn)題：量子理想氣體。第三章和第四章分別致力于多粒子體系和場(chǎng)的二次量子化。第五章研究玻色一愛(ài)因斯坦凝結(jié)。第六章研究一批量子統(tǒng)計(jì)中的反問(wèn)題，它們的陳氏（或Mobius-Chen）嚴(yán)格解公式，戴氏嚴(yán)格解公式及其漸近行為控制理論和反演理論的具體實(shí)現(xiàn)，特別是由高溫超導(dǎo)體的實(shí)際比熱數(shù)據(jù)，直接反演出聲子譜。第七章是Fermi和B0se的二次型哈密頓量的統(tǒng)一的對(duì)角化定理。

內(nèi)容概要

　　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 Chens exact solution formulas， Dais exact solution formulas，asymptotic behavior control theory， and concrete realizations of the inversion theories）， an introduction to the theory of Greens 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.

作者簡(jiǎn)介

　　戴顯熹，1938年5月生于溫州。1961年7月畢業(yè)于復(fù)旦大學(xué)物理系。1985年起任復(fù)旦大學(xué)物理系教授，1986年起任博士生導(dǎo)師。長(zhǎng)期從事量子統(tǒng)計(jì)和理論物理方法研究，發(fā)表學(xué)術(shù)論文100多篇。　　自1978年以來(lái)，從事研究生的量子統(tǒng)計(jì)與高等統(tǒng)計(jì)課程教學(xué)，以及本科生的電動(dòng)力學(xué)、量子力學(xué)、數(shù)理方法、超導(dǎo)物理、理論物理方法等課程的教學(xué)。曾獲得楊振寧教授授予的Glorious Sun獎(jiǎng)金，曾以物理學(xué)中奇性問(wèn)題研究獲教育部授予的科學(xué)進(jìn)步獎(jiǎng)（二等）等。1980年來(lái)應(yīng)邀訪問(wèn)過(guò)美國(guó)的休斯頓大學(xué)、紐約州立大學(xué)理論物理（楊振寧）研究所、德克薩斯超導(dǎo)中心、楊伯翰大學(xué)等，曾任楊伯翰大學(xué)客座教授。在量子統(tǒng)計(jì)、物理學(xué)中奇性問(wèn)題、一些逆問(wèn)題的嚴(yán)格解及其統(tǒng)一理論和漸近行為控制理論等方面作過(guò)較為系統(tǒng)的研究，首次由一材料的比熱實(shí)際數(shù)據(jù)中反演出聲子譜。

書(shū)籍目錄

Chapter 1 Fundamental Principles1.1 Introduction： The Characters of Thermodynamics and Statistical Physics and Their Relationship1.2 Basic Thermodynamic Identities1.3 Fundamental Principles and Conclusions of Classical Statistics1.3.1 Microscopic and Macroscopic Descriptions， Statistical Distribution Functions1.3.2 Liouville Theorem1.3.3 Statistical Independence1.3.4 Microscopical Canonical， Canonical and Grand Canonical Ensembles1.4 Boltzmann Gas1.5 Density Matrix1.5.1 Density Matrix1.5.2 Some General Properties of the Density Matrix1.6 Liouville Theorem in Quantum Statistics1.7 Canonical Ensemble1.8 Grand Canonical Ensemble1.8.1 Fundamental Expression of the Grand Canonical Ensemble1.8.2 Derivation of the Fundamental Thermodynamic Identity1.9 Probability Distribution and Slater Sum1.9.1 Meaning of the Diagonal Elements of the Density Matrix1.9.2 Slater Summation1.9.3 Example ： Probability of the Harmonic Ensemble1.10 Theory of the Reduced Density MatrixChapter 2 The Perfect Gas in Quantum Statistics2.1 Indistinguishability Principle for Identical Particles2.2 Bose Distribution and Fermi Distribution2.2.1 Perfect Gases in Quantum Statistics2.2.2 Bose Distribution2.2.3 Fermi Distribution2.2.4 Comparison of Three Distributions；Gibbs Paradox AgainChapter 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 Greens FunctionsChapter 8 A Unified Diagonalization Theorem for Quadratic HamiltonianChapter 9 Functional Integral Approach： A Third Formulation of Quantum Statistical MechanicsReferencesIndex

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