統(tǒng)計(jì)力學(xué)

內(nèi)容概要

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.

書籍目錄

PrefaceChapter 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  ProblemsChapter 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  ProblemsChapter 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  ProblemsChapter 4 Equilibrium Quantum Statistical Mechanics  4.1 Resume of Quantum Mechanics  ……Chapter 5 Identical Particles in Quantum Statistical Me-chanicsChapter 6 Spin Hamiltonians Ⅱ：QuantumChapter 7 Phase Transitions and Critical PhenomenaChapter 8 Model Systems,Scaling Laws and Mean Field TheoriesChapter 9 Superconductivity & SuperfluidityChapter 10 The Renormalization Group and Critical Phe-nomenaAppendix A Mathematical Digression Ⅰ:Differentiable Man-ifolds and Exterior CalculusAppendix B Mathematical Digression Ⅱ:Some Mathematics of Hilbert Spaces.Appendix C Linear Stability Theory.Appendix D Eigenvalue and Eigenvector Problems for Non-Symmetric MatricesBibliographyIndex

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