平衡統(tǒng)計物理學(xué)

內(nèi)容概要

　　這是針對從事物理、化學(xué)和材料科學(xué)的研究生和高年級本科生的專業(yè)需求編寫的統(tǒng)計物理教材。早在1980年，作者們發(fā)現(xiàn)由K.G.Wilson率先將重整化群方法引入臨界現(xiàn)象并取得成功之后，凝聚態(tài)物理的研究進入了飛速發(fā)展的黃金時代，因此認為研究生的早期教學(xué)工作應(yīng)當(dāng)反映這方面的動態(tài)。為此于1989年率先由Prentice-Hall出版公司出版了反映這方面特色的《平衡統(tǒng)計物理學(xué)》，1994年經(jīng)過修訂，轉(zhuǎn)到World Scientific出版了本書第一版，1999年出版了第二版，現(xiàn)在呈現(xiàn)在讀者面前的是2003年的版本?！　∪珪卜?1章，前兩章分別復(fù)習(xí)熱力學(xué)和統(tǒng)計系統(tǒng)理論，這部分內(nèi)容既是讀者學(xué)習(xí)后面各章的基礎(chǔ)，也是為了本科期間沒有接觸過熱力學(xué)和統(tǒng)計物理的學(xué)生設(shè)計的。兩章都有大量習(xí)題，可以幫助讀者加深理解。后面各章分別講述平均場和朗道理論、致密氣體和液體、臨界現(xiàn)象的二維伊辛模型、級數(shù)展開、標(biāo)度律、重整化群方法等。第七章介紹動力學(xué)模擬方法。八、九、十、十一各章介紹統(tǒng)計物理最活躍的應(yīng)用領(lǐng)域:聚合物和薄膜、量子流體、線性響應(yīng)理論、無序系統(tǒng)等。由于本書的后半部分涉及二次量子化的概念，因此在附錄中補充了占有數(shù)表象的內(nèi)容。本書每章都有不少的習(xí)題，越到后面各章，習(xí)題的難度越來越有挑戰(zhàn)性。作者們還專門編寫了《習(xí)題解答》，有需要的教師或讀者可通過互聯(lián)網(wǎng)（http://www.worldscibooks.com/physics/4485.html）查找。

作者簡介

Michael Plischke，加拿大Simon Fraser大學(xué)物理系主任，教授。芝加哥Loyola大學(xué)物理學(xué)學(xué)士，Yale大學(xué)物理學(xué)碩士，Yeshiva大學(xué)物理學(xué)博士，長期從事凝聚態(tài)物理研究，并給碩士生和本科生講授統(tǒng)計力學(xué)。Equilibrium Statistical Physics和Physics and Chemistry of Disordered S

書籍目錄

ContentsPreface to the First EditionPreface to the Second Edition1 Review of Thermodynamics 　1.1 State Variables and Equations of State 　1.2 Laws of Thermodynamics 　1.2.1 First law 　1.2.2 Second law 　1.3 Thermodynamic Potentials 　1.4 Gibbs-Duhem and Maxwell Relations 　1.5 Response Functions 　1.6 Conditions for Equilibrium and Stability 　1.7 Thermodynamics of Phase Transitions 　1.8 Problems 2 Statistical Ensembles 　2.1 Isolated Systems: MicrocanonicalEnsemble 　2.2 Systems at Fixed Temperature: Canonical Ensemble 　2.3 Grand Canonical Ensemble 　2.4 Quantum Statistics 　2.4.1 Harmonic oscillator 　2.4.2 Noninteracting fermions 　2.4.3 Noninteracting bosons 　2.4.4 Density matrix 　2.5 Maximum Entropy Principle 　2.6 Thermodynamic Variational Principles 　2.7 Problems 3 Mean Field and Landau Theory 　3.1 Mean Field Theory of the Ising Model 　3.2 Bragg-Williams Approximation 　3.3 Order Disorder Transition 　3.4 Bethe Approximation 　3.5 Critical Behavior of Mean Field Theories 　3.6 Ising Chain: Exact Solution 　3.7 Landau Theory of Phase Transitions 　3.8 Example of Symmetry Considerations: Maier-Saupe Model 　3.9 Landau Theory of Tricritical Points 　3.10 Landau-Ginzburg Theory for Fluctuations 　3.11 Multicomponent Order Parameters: n-Vector Model 　3.12 Mean Field Theory of Fluids: Van der Waals Approach 　3.13 Problems 4 Dense Gases and Liquids 　4.1 Virial Expansion 　4.2 Distribution Functions 　　4.2.1 Pair correlation function 　　4.2.2 BBGKY hierarchy 　　4.2.3 Ornstein-Zernike equation 　4.3 Perturbation Theory 　4.4 Inhomogeneous Liquids　　4.4.1 Liquid-vapor interface 　　4.4.2 Capillary waves 　4.5 Density-Functional Theory 　　4.5.1 Functional differentiation 　　4.5.2 Free-energy functionals and correlation functions 　　4.5.3 Applications 　4.6 Problems 5 Critical Phenomena I 　5.1 Ising Model in Two Dimensions 　　5.1.1 Transfer matrix 　　5.1.2 Transformation to an interacting fermion problem 　　5.1.3 Calculation of eigenvalues 　　5.1.4 Thermodynamic functions 　　5.1.5 Concluding remarks 　5.2 Series Expansions 　　5.2.1 High-temperature expansions 　　5.2.2 Low-temperature expansions　　5.2.3 Analysis of series 　5.3 Scaling 　　5.3.1 Thermodynamic considerations 　　5.3.2 Scaling hypothesis 　　5.3.3 Kadanoff block spins　5.4 Finite-Size Scaling 　5.5 Universality 　5.6 Kosterlitz-Thouless Transition 　5.7 Problems 6 Critical Phenomena II: The Renormalization Group 　6.1 The Ising Chain Revisited 　6.2 Fixed Points 　6.3 Position Space Renormalization: Cumulant Method 　　6.3.1 First-order approximation 　　6.3.2 Second-order approximation 　6.4 Other Position Space RenormalizationGroup Methods 　　6.4.1 Finite lattice methods 　　6.4.2 Adsorbed monolayers: Ising antiferromagnet 　　6.4.3 Monte Carlo renormalization 　6.5 Phenomenological Renormalization Group 　6.6 The e-Expansion 　　6.6.1 The Gaussian model 　　6.6.2 The S4 model 　　6.6.3 Critical exponents to order ε 　　6.6.4 Conclusion 　6.7 Problems 7 Simulations　7.1 Molecular Dynamics　7.2 Monte Carlo Method　　7.2.1 Markov processes　　7.2.2 Detailed balance and the Metropolis algorithm　　7.2.3 Histogram methods　7.3 Data Analysis　　7.3.1 Fluctuations　　7.3.2 Error estimates　　7.3.3 Extrapolation to the thermodynamic limit 　7.4 The Hopfield Model of Neural Nets 　7.5 Simulated Quenching and Annealing 　7.6 Problems 8 Polymers and Membranes 　8.1 Linear Polymers 　　8.1.1 The freely jointed chain 　　8.1.2 The Gaussian chain 　8.2 Excluded Volume Effects: Flory Theory 　8.3 Polymers and the n-Vector Model 　8.4 Dense Polymer Solutions 　8.5 Membranes 　　8.5.1 Phantom membranes 　　8.5.2 Self-avoiding membranes 　　8.5.3 Liquid membranes 　8.6 Problems 9 Quantum Fluids　9.1 Bose Condensation　9.2 Superfluidity　　9.2.1 Qualitative features of superfluidity　　9.2.2 Bogoliubov theory of the aHe excitation spectrum　9.3 Superconductivity　　9.3.1 Cooper problem　　9.3.2 BCS ground state　　9.3.3 Finite-temperature BCS theory　　9.3.4 Landau-Ginzburg theory of superconductivity　9.4 Problems10 Linear Response Theory 　10.1 Exact Results 378　　10.1.1 Generalized susceptibility and the structure factor　　10.1.2 Thermodynamic properties　　10.1.3 Sum rules and inequalities　10.2 Mean Field Response　　10.2.1 Dielectric function of the electron gas　　10.2.2 Weakly interacting Bose gas　　10.2.3 Excitations of the Heisenberg ferromagnet　　10.2.4 Screening and plasmons 　　10.2.5 Exchange and correlation energy 　　10.2.6 Phonons in metals 　10.3 Entropy Production, the Kubo Formula, and the Onsager Relations for Transport Coefficients 　　10.3.1 Kubo formula 　　10.3.2 Entropy production and generalized currents and forces 　　10.3.3 Microscopic reversibility: Onsager relations 　10.4 The Boltzmann Equation 　　10.4.1 Fields, drift and collisions 　　10.4.2 DC conductivity of a metal 　　10.4.3 Thermal conductivity and thermoelectric effects 　10.5 Problems 11 Disordered Systems 　11.1 Single-Particle States in Disordered Systems 　　11.1.1 Electron states in one dimension 　　11.1.2 Transfer matrix 　　11.1.3 Localization in three dimensions 　　11.1.4 Density of states 　11.2 Percolation 　　11.2.1 Scaling theory of percolation 　　11.2.2 Series expansions and renormalization group 　　11.2.3 Conclusion 　11.3 Phase Transitions in Disordered Materials 　　11.3.1 Statistical formalism and the replica trick 　　11.3.2 Nature of phase transitions 　11.4 Strongly Disordered Systems 　　11.4.1 Molecular glasses 　　11.4.2 Spin glasses 　　11.4.3 Sherrington-Kirkpatrick model 　11.5 Problems Appendix: Occupation Number RepresentationBibliographyIndex

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