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统计力学：中级课程STATISTICAL MECHANICS

统计力学：中级课程STATISTICAL MECHANICS

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作者: Giuseppe Morandi , E. Ercolessi , F. Napoli

出版社: Penguin

出版时间: 2001-12

版次: 1

ISBN: 9789810244774

定价: 451.00

装帧: 平装

开本: 其他

纸张: 胶版纸

页数: 648页

分类: 教育

This book covers the foundations of classical thermodynamics, with emphasis on the use of differential forms of classical and quantum statistical mechanics, and also on the foundational aspects. In both contexts, a number of applications are considered in detail, such as the general theory of response, correlations and fluctuations, and classical and quantum spin systems. In the quantum case, a self-contained introduction to path integral methods is given. In addition, the book discusses phase transitions and critical phenomena, with applications to the Landau theory and to the Ginzburg-Landau theory of superconductivity, and also to the phenomenon of Bose condensation and of superfluidity. Finally, there is a careful discussion on the use of the renormalization group in the study of critical phenomena. Preface

Chapter 1 Thermodynamics

  1.1 A Recollection of Basic Notions in Classical Thermodynamics

    1.1.1 The Fundamental Equation of Thermodynamics

  1.2 Thermodynamic Potentials, ...Stability Conditions

  1.3 A Mathematical Digression: Integrating Factors and

  1A An Exercise in the Use of the Gibbs-Duhem Relation: the Ideal Monoatomic Gas

  1B Thermodynamics of Paramagnetic Bodies

  1C Some Relations on Partial Derivatives & Jacobians

  1D A Digression on: Integrability Conditions

  Problems

Chapter 2 Equilibrium Classical Statistical Mechanics

  2.1 Foundations of Classical Statistical Mechanics

    2.1.1 A resume of Hamiltonian Dynamics

    2.1.2 Canonical Transformations

    2.1.3 The Heisenberg and Schr5dinger Pictures in Classical Dynamics

    2.1.4  Integrable Dynamical Systems and Perturbations

    2.1.5  The Ergodic Hypothesis and the Foundations of Classical Statistical Mechanics

  2.2  Statistical Ensembles in CSM: Micro-canonical Ensemble

    2.2.1  The Entropy Function

  2.3 Statistical Ensembles in CSM: Canonical and Grand-Canonical Ensembles

    2.3.1 The Canonical Ensemble

    2.3.2 The Grand-Canonical Ensemble

    2.3.3 Some Applications

    2.3.4 General Remarks

  2.4 Response, Correlations and Fluctuations: I Classical

    2.4.1 Symmetry Properties of Correlation Fhnctions

    2.4.2 Fourier Transforms of Correlation Functions

    2.4.3 Generating Functionals and Static Generalized Suscep-tibilities

    2.4.4 Linear Response Theory

    2.4.5 The Classical Fluctuation-Dissipation Theorem

  2A Harmonic Oscillators & Ergodicity

  2B The Volume Phase Space for a Perfect Gas

  2C Density-Density Correlation Function of a Perfect Gas

  Problems

Chapter 3 Spin Hamiltonians Ⅰ: Classical

  3.1 Spin Hamiltonians

  3.2 Gaussian Identities for Spin Hamiltonians

  3.3 Mean Field Theory and Phase Transitions

    3.3.1  MFA for Ising Model

    3.3.2  MFA for Heisenberg Model

  3.4 Linearized Spin Dynamics: Spin Waves, Response and Correla- tions

  3.5 SSB, Goldstone and Mermin-Wagner Theorems

    3.5.1 The Goldstone Theorem

    3.5.2 The Mermin-Wagner Theorem

  3A Poisson Description of Spin Dynamics

  3B Perturbation expansions and the Classical Analogue of Wick's Theorem

  3C  "Conventional" Mean Field Theory

  3D  Some Group-Theoretical Aspects Related to SSB

  Problems

Chapter 4 Equilibrium Quantum Statistical Mechanics

  4.1 Resume of Quantum Mechanics

  ……

Chapter 5 Identical Particles in Quantum Statistical Me-chanics

Chapter 6 Spin Hamiltonians Ⅱ：Quantum

Chapter 7 Phase Transitions and Critical Phenomena

Chapter 8 Model Systems,Scaling Laws and Mean Field Theories

Chapter 9 Superconductivity & Superfluidity

Chapter 10 The Renormalization Group and Critical Phe-nomena

Appendix A Mathematical Digression Ⅰ:Differentiable Man-ifolds and Exterior Calculus

Appendix B Mathematical Digression Ⅱ:Some Mathematics of Hilbert Spaces.

Appendix C Linear Stability Theory.

Appendix D Eigenvalue and Eigenvector Problems for Non-Symmetric Matrices

Bibliography

Index
内容简介:
This book covers the foundations of classical thermodynamics, with emphasis on the use of differential forms of classical and quantum statistical mechanics, and also on the foundational aspects. In both contexts, a number of applications are considered in detail, such as the general theory of response, correlations and fluctuations, and classical and quantum spin systems. In the quantum case, a self-contained introduction to path integral methods is given. In addition, the book discusses phase transitions and critical phenomena, with applications to the Landau theory and to the Ginzburg-Landau theory of superconductivity, and also to the phenomenon of Bose condensation and of superfluidity. Finally, there is a careful discussion on the use of the renormalization group in the study of critical phenomena.
目录:
Preface

Chapter 1 Thermodynamics

  1.1 A Recollection of Basic Notions in Classical Thermodynamics

    1.1.1 The Fundamental Equation of Thermodynamics

  1.2 Thermodynamic Potentials, ...Stability Conditions

  1.3 A Mathematical Digression: Integrating Factors and

  1A An Exercise in the Use of the Gibbs-Duhem Relation: the Ideal Monoatomic Gas

  1B Thermodynamics of Paramagnetic Bodies

  1C Some Relations on Partial Derivatives & Jacobians

  1D A Digression on: Integrability Conditions

  Problems

Chapter 2 Equilibrium Classical Statistical Mechanics

  2.1 Foundations of Classical Statistical Mechanics

    2.1.1 A resume of Hamiltonian Dynamics

    2.1.2 Canonical Transformations

    2.1.3 The Heisenberg and Schr5dinger Pictures in Classical Dynamics

    2.1.4  Integrable Dynamical Systems and Perturbations

    2.1.5  The Ergodic Hypothesis and the Foundations of Classical Statistical Mechanics

  2.2  Statistical Ensembles in CSM: Micro-canonical Ensemble

    2.2.1  The Entropy Function

  2.3 Statistical Ensembles in CSM: Canonical and Grand-Canonical Ensembles

    2.3.1 The Canonical Ensemble

    2.3.2 The Grand-Canonical Ensemble

    2.3.3 Some Applications

    2.3.4 General Remarks

  2.4 Response, Correlations and Fluctuations: I Classical

    2.4.1 Symmetry Properties of Correlation Fhnctions

    2.4.2 Fourier Transforms of Correlation Functions

    2.4.3 Generating Functionals and Static Generalized Suscep-tibilities

    2.4.4 Linear Response Theory

    2.4.5 The Classical Fluctuation-Dissipation Theorem

  2A Harmonic Oscillators & Ergodicity

  2B The Volume Phase Space for a Perfect Gas

  2C Density-Density Correlation Function of a Perfect Gas

  Problems

Chapter 3 Spin Hamiltonians Ⅰ: Classical

  3.1 Spin Hamiltonians

  3.2 Gaussian Identities for Spin Hamiltonians

  3.3 Mean Field Theory and Phase Transitions

    3.3.1  MFA for Ising Model

    3.3.2  MFA for Heisenberg Model

  3.4 Linearized Spin Dynamics: Spin Waves, Response and Correla- tions

  3.5 SSB, Goldstone and Mermin-Wagner Theorems

    3.5.1 The Goldstone Theorem

    3.5.2 The Mermin-Wagner Theorem

  3A Poisson Description of Spin Dynamics

  3B Perturbation expansions and the Classical Analogue of Wick's Theorem

  3C  "Conventional" Mean Field Theory

  3D  Some Group-Theoretical Aspects Related to SSB

  Problems

Chapter 4 Equilibrium Quantum Statistical Mechanics

  4.1 Resume of Quantum Mechanics

  ……

Chapter 5 Identical Particles in Quantum Statistical Me-chanics

Chapter 6 Spin Hamiltonians Ⅱ：Quantum

Chapter 7 Phase Transitions and Critical Phenomena

Chapter 8 Model Systems,Scaling Laws and Mean Field Theories

Chapter 9 Superconductivity & Superfluidity

Chapter 10 The Renormalization Group and Critical Phe-nomena

Appendix A Mathematical Digression Ⅰ:Differentiable Man-ifolds and Exterior Calculus

Appendix B Mathematical Digression Ⅱ:Some Mathematics of Hilbert Spaces.

Appendix C Linear Stability Theory.

Appendix D Eigenvalue and Eigenvector Problems for Non-Symmetric Matrices

Bibliography

Index

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