INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition
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1 INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition Kerson Huang CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group an Informa business A CHAPMAN & HALL BOOK
2 Contents Preface xiii 1 A Macroscopic View of Matter Viewing the World at Different Scales Thermodynamics The Thermodynamic Limit Thermodynamic Transformations Classic Ideal Gas First Law of Thermodynamics Magnetic Systems 9 Problems 11 References 13 2 Heat and Entropy The Heat Equations Applications to Ideal Gas Carnot Cycle Second Law of Thermodynamics Absolute Temperature Temperature as Integrating Factor Entropy Entropy of Ideal Gas The Limits of Thermodynamics 27 Problems 27 3 Using Thermodynamics The Energy Equation Some Measurable Coefficients Entropy and Loss TS Diagram Condition for Equilibrium Helmholtz Free Energy Gibbs Potential Maxwell Relations Chemical Potential 42 Problems 43 vii
3 Vlll Contents 4 Phase Transitions First-Order Phase Transition Condition for Phase Coexistence Clapeyron Equation Van der Waals Equation of State Virial Expansion Critical Point Maxwell Construction Scaling Nucleation and Spinodal Decomposition 57 Problems 60 References 63 5 The Statistical Approach The Atomic View Random Walk Phase Space Distribution Function Ergodic Hypothesis Statistical Ensemble Microcanonical Ensemble Correct Boltzmann Counting Distribution Entropy: Boltzmann's H The Most Probable Distribution Information Theory: Shannon Entropy 78 Problems 80 References 82 6 Maxwell-Boltzmann Distribution Determining the Parameters Pressure of Ideal Gas Equipartition of Energy Distribution of Speed Entropy Derivation of Thermodynamics Fluctuations The Boltzmann Factor Time's Arrow 92 Problems 93 References 97 7 Transport Phenomena Collisionless and Hydrodynamic Regimes Maxwell's Demon Nonviscous Hydrodynamics 101
4 Contents ix 7.4 Sound Wave Diffusion Heat Conduction Viscosity Navier-Stokes Equation 107 Problems 109 References ПО 8 Canonical Ensemble Ill 8.1 Review of the Microcanonical Ensemble Ill 8.2 Classical Canonical Ensemble Ill 8.3 The Partition Function Connection with Thermodynamics Energy Fluctuations Minimization of Free Energy Classical Ideal Gas 118 Problems Grand Canonical Ensemble The Particle Reservoir Grand Partition Function Number Fluctuations Connection with Thermodynamics Parametric Equation of State and Virial Expansion Critical Fluctuations Pair Creation 128 Problems Noise Thermal Fluctuations Nyquist Noise Brownian Motion Einstein's Theory Diffusion Einstein's Relation Molecular Reality Fluctuation and Dissipation Brownian Motion of the Stock Market 145 Problems 148 References Stochastic Processes Randomness and Probability Binomial Distribution Poisson Distribution 154
5 X Contents 11.4 Gaussian Distribution Central Limit Theorem Shot Noise 157 Problems 160 References Time-Series Analysis Ensemble of Paths Ensemble Average Power Spectrum and Correlation Function Signal and Noise Transition Probabilities Markov Process Fokker-Planck Equation The Monte Carlo Method Simulation of the Ising Model 176 Problems 179 References The Langevin Equation The Equation and Solution Energy Balance Fluctuation-Dissipation Theorem Diffusion Coefficient and Einstein's Relation Transition Probability: Fokker-Planck Equation Heating by Stirring: Forced Oscillator in Medium 189 Problems Quantum Statistics Thermal Wavelength Identical Particles Occupation Numbers Spin Microcanonical Ensemble Fermi Statistics Bose Statistics Determining the Parameters Pressure Entropy Free Energy Equation of State Classical Limit 208 Problems 210 Reference 212
6 Contents xi 15 Quantum Ensembles Incoherent Superposition of States Density Matrix Canonical Ensemble (Quantum-Mechanical) Grand Canonical Ensemble (Quantum-Mechanical) Occupation Number Fluctuations Photon Bunching 220 Problems 221 References The Fermi Gas Fermi Energy Ground State Fermi Temperature Low-Temperature Properties Particles and Holes Electrons in Solids Semiconductors 233 Problems The Bose Gas Photons Bose Enhancement Phonons Debye Specific Heat Electronic Specific Heat Conservation of Particle Number 245 Problems 246 References Bose-Einstein Condensation Macroscopic Occupation The Condensate Equation of State Specific Heat How a Phase is Formed Liquid Helium 259 Problems 260 References The Order Parameter The Essence of Phase Transitions Ginsburg-Landau Theory Relation to Microscopic Theory Functional Integration and Differentiation 268
7 xii Contents 19.5 Second-Order Phase Transition Mean-Field Theory Critical Exponents The Correlation Length First-Order Phase Transition Cahn-Hilliard Equation 278 Problems 278 References Superfluidity Condensate Wave Function Spontaneous Symmetry Breaking Mean-Field Theory Observation of Bose-Einstein Condensation Quantum Phase Coherence Superfluid Flow Phonons: Goldstone Mode 289 Problems 290 References Superconductivity Meissner Effect Magnetic Flux Quantum Josephson Junction DC Josephson Effect AC Josephson Effect Time-Dependent Vector Potential The SQUID Broken Symmetry 302 Problems 303 References 303 Appendix 305 Index 313
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