图书信息

作者：[英]Brian Cowan

定价：35.00元

页数：338页

ISBN：7-309-05201-3/O.373

字数：250千字

开本：32 开

装帧：平装

出版日期：2006年11月

内容提要

全书用一种统一的观点处理热力学和统计物理论题。第一、第二章分别讲述统计力学的方法论和理想体系的实际计算。其中差不多有一半内容属于本科期间已有的基础知识，但采用更高的、完全用统一的观点，看待热力学和统计力学。第三章非理想气体，重点讲述维里展开、配分函数、节流和状态方程。第四章相变，介绍相图、对称性、序参量、临界指数、标度理论、一级相变、二级相变、伊辛模型、朗道理论、铁电体、二元混合物、量子相变、平均场理论等等。这是全书的重点。第五章讲述涨落和动力学行为，重点是涨落的关联特性、布朗运动、朗之万方程和线性响应理论。1

图书目录

ContentsPreface1 The Methodology of Statistical Mechanics1.1 Terminology and Methodology1.1.1 Approaches to the subject1.1.2 Description of states1.1.3 Extensivity and the thermodynamic limit1.2 The Fundamental Principles1.2.1 The laws of thermodynamics1.2.2 Probabilistic interpretation of the First Law1.2.3 Microscopic basis for entropy1.3 Interactions —The Conditions for Equilibrium1.3.1 Thermal interaction—Temperature1.3.2 Volume change—Pressure1.3.3 Particle interchange—Chemical potential1.3.4 Thermal interaction with the rest of the world—The Boltzmann factor1.3.5 Particle and energy exchange with the rest of the world —The Gibbs factor1.4 Thermodynamic Averages1.4.1 The partition function1.4.2 Generalised expression for entropy1.4.3 Free energy1.4.4 Thermodynamic variables1.4.5 Fluctuations1.4.6 The grand partition function1.4.7 The grand potential1.4.8 Thermodynamic variables1.5 Quantum Distributions1.5.1 Bosons and fermions1.5.2 Grand potential for identical particles1.5.3 The Fermi distribution1.5.4 The Bose distribution1.5.5 The classical limit—The Maxwell distributior1.6 Classical Statistical Mechanics1.6.1 Phase space and classical states1.6.2 Boltzmann and Gibbs phase spaces1.6.3 The Fundamental Postulate in the classical case1.6.4 The classical partition function1.6.5 The equipartition theorem1.6.6 Consequences of equipartition1.6.7 Liouville's theorem1.6.8 Boltzmann's H theorem1.7 The Third Law of Thermodynamics1.7.1 History of the Third Law1.7.2 Entropy1.7.3 Quantum viewpoint1.7.4 Unattainability of absolute zero1.7.5 Heat capacity at low temperatures1.7.6 Other consequences of the Third Law1.7.7 Pessimist's statement of the laws of thermodynamics2 Practical Calculations with Ideal Systems2.1 The Density of States2.1.1 Non-interacting systems2.1.2 Converting sums to integrals2.1.3 Enumeration of states2.1.4 Counting states2.1.5 General expression for the density of states2.1.6 General relation between pressure and energy2.2 Identical Particles2.2.1 Indistinguishability2.2.2 Classical approximation2.3 Ideal Classical Gas2.3.1 Quantum approach2.3.2 Classical approach2.3.3 Thermodynamic properties2.3.4 The l/N! term in the partition function2.3.5 Entropy of mixing2.4 Ideal Fermi Gas2.4.0 Methodology for quantum gases2.4.1 Fermi gas at zero temperature2.4.2 Fermi gas at low temperatures—simple model2.4.3 Fermi gas at low temperatures—series expansionChemical potentialInternal energyThermal capacity2.4.4 More general treatment of low temperature heat capacity2.4.5 High temperature behaviour—the classical limit2.5 Ideal Bose Gas2.5.1 General procedure for treating the Bose gas2.5.2 Number of particles—chemical potential2.5.3 Low temperature behaviour of Bose gas2.5.4 Thermal capacity of Bose gas—below Tc2.5.5 Comparison with superfluid4 He and other systems2.5.6 Two-fluid model of superfluid 4He2.5.7 Elementary excitations2.6 Black Body Radiation—The Photon Gas2.6.1 Photons as quantised electromagnetic waves2.6.2 Photons in thermal equilibrium—black body radiation2.6.3 Planck's formula2.6.4 Internal energy and heat capacity2.6.5 Black body radiation in one dimension2.7 Ideal Paramagnet2.7.1 Partition function and free energy2.7.2 Thermodynamic properties2.7.3 Negative temperatures2.7.4 Thermodynamics of negative temperatures3 Non-Ideal Gases3.1 Statistical Mechanics3.1.1 The partition function3.1.2 Cluster expansion3.1.3 Low density approximation3.1.4 Equation of state3.2 The Virial Expansion3.2.1 Virial coefficients3.2.2 Hard core potential3.2.3 Square-well potential3.2.4 Lennard-Jones potential3.2.5 Second virial coefficient for Bose and Fermi gas3.3 Thermodynamics3.3.1 Throttling3.3.2 Joule-Thomson coefficient3.3.3 Connection with the second virial coefficient..3.3.4 Inversion temperature3.4 Van der Waals Equation of State3.4.1 Approximating the partition function3.4.2 Van der Waals equation3.4.3 Microscopic "derivation" of parameters3.4.4 Virial expansion3.5 Other Phenomenological Equations of State3.5.1 The Dieterici equation3.5.2 Virial expansion3.5.3 The Berthelot equation4 Phase Transitions4.1 Phenomenology4.1.1 Basic ideas4.1.2 Phase diagrams4.1.3 Symmetry4.1.4 Order of phase transitions4.1.5 The order parameter4.1.6 Conserved and non-conserved order parameters4.1.7 Critical exponents4.1.8 Scaling theory4.1.9 Scaling of the free energy4.2 First-Order Transition—An Example4.2.1 Coexistence4.2.2 Van der Waals fluid4.2.3 The Maxwell construction4.2.4 The critical point4.2.5 Corresponding states4.2.6 Dieterici's equation4.2.7 Quantum mechanical effects4.3 Second-Order Transition—An Example4.3.1 The ferromagnet4.3.2 The Weiss model4.3.3 Spontaneous magnetisation4.3.4 Critical behaviour4.3.5 Magnetic susceptibility4.3.6 Goldstone modes4.4 The Ising and Other Models4.4.1 Ubiquity of the Ising model4.4.2 Magnetic case of the Ising model4.4.3 Ising model in one dimension4.4.4 Ising model in two dimensions4.4.5 Mean field critical exponents4.4.6 The XY model4.4.7 The spherical model4.5 Landau Treatment of Phase Transitions4.5.1 Landau free energy4.5.2 Landau free energy for the ferromagnet4.5.3 Landau theory—second-order transitions4.5.4 Thermal capacity in the Landau model4.5.5 Ferromagnet in a magnetic field4.6 Ferroelectricity4.6.1 Description of the phenomenon4.6.2 Landau free energy4.6.3 Second-order case4.6.4 First-order case4.6.5 Entropy and latent heat at the transition4.6.6 Soft modes4.7 Binary Mixtures4.7.1 Basic ideas4.7.2 Model calculation4.7.3 System energy4.7.4 Entropy4.7.5 Free energy4.7.6 Phase separation—the lever rule4.7.7 Phase separation curve—the binodal4.7.8 The spinodal curve4.7.9 Entropy in the ordered phase4.7.10 Thermal capacity in the ordered phase4.7.11 Order of the transition and the critical point4.7.12 The critical exponent β4.8 Quantum Phase Transitions4.8.1 Introduction4.8.2 The transverse Ising model4.8.3 Revision of mean field Ising model4.8.4 Application of a transverse field4.8.5 Transition temperature4.8.6 Quantum critical behaviour4.8.7 Dimensionality and critical exponents4.9 Retrospective4.9.1 The existence of order4.9.2 Validity of mean field theory4.9.3 Features of different phase transition models5 Fluctuations and Dynamics5.1 Fluctuations5.1.1 Probability distribution functions5.1.2 Mean behaviour of fluctuations5.1.3 The autocorrelation function5.1.4 The correlation time5.2 Brownian Motion5.2.1 Kinematics of a Brownian particle5.2.2 Short time limit5.2.3 Long time limit5.3 Langevin's Equation5.3.1 Introduction5.3.2 Separation of forces5.3.3 The Langevin equation5.3.4 Mean square velocity and equipartition5.3.5 Velocity autocorrelation function5.3.6 Electrical analogue of the Langevin equation5.4 Linear Response—Phenomenology5.4.1 Definitions5.4.2 Response to a sinusoidal excitation5.4.3 Fourier representation5.4.4 Response to a step excitation5.4.5 Response to a delta function excitation5.4.6 Consequence of the reality of X(t)5.4.7 Consequence of causality5.4.8 Energy considerations5.4.9 Static susceptibility5.4.10 Relaxation time approximation5.5 Linear Response—Microscopics5.5.1 Onsager's hypothesis5.5.2 Nyquist's theorem5.5.3 Calculation of the step response function5.5.4 Calculation of the autocorrelation functionAppendixesAppendix I The Gibbs-Duhem RelationA.1.1 Homogeneity of the fundamental relationA.1.2 The Euler relationA.1.3 A caveatA.1.4 The Gibbs-Duhem relationAppendix 2 Thermodynamic PotentialsA.2.1 Equilibrium statesA.2.2 Constant temperature (and volume): the Helmholtz potentialA.2.3 Constant pressure and energy: the Enthalpy functionA.2.4 Constant pressure and temperature: the Gibbs free energyA.2.5 Differential expressions for the potentialsA.2.6 Natural variables and the Maxwell relationsAppendix 3 Mathematica NotebooksA.3.1 Chemical potential of Fermi gas at low temperaturesA.3.2 Internal energy of the Fermi gas at low temperaturesA.3.3 Fugacity of the ideal gas at high temperatures—Fermi, Maxwell and Bose casesA.3.4 Internal energy of the ideal gas at high temperatures—Fermi, Maxwell and Bose casesAppendix 4 Evaluation of the Correlation Function IntegralA.4.1 Initial domain of integrationA.4.2 Transformation of variablesA.4.3 Jacobian of the transformationIndex1

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