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
Contents Preface xiii 1 A Macroscopic View of Matter 1 1.1 Viewing the World at Different Scales 1 1.2 Thermodynamics 2 1.3 The Thermodynamic Limit 3 1.4 Thermodynamic Transformations 4 1.5 Classic Ideal Gas 7 1.6 First Law of Thermodynamics 8 1.7 Magnetic Systems 9 Problems 11 References 13 2 Heat and Entropy 15 2.1 The Heat Equations 15 2.2 Applications to Ideal Gas 16 2.3 Carnot Cycle 19 2.4 Second Law of Thermodynamics 20 2.5 Absolute Temperature 21 2.6 Temperature as Integrating Factor 22 2.7 Entropy 25 2.8 Entropy of Ideal Gas 26 2.9 The Limits of Thermodynamics 27 Problems 27 3 Using Thermodynamics 33 3.1 The Energy Equation 33 3.2 Some Measurable Coefficients 34 3.3 Entropy and Loss 35 3.4 TS Diagram 37 3.5 Condition for Equilibrium 39 3.6 Helmholtz Free Energy 40 3.7 Gibbs Potential 41 3.8 Maxwell Relations 42 3.9 Chemical Potential 42 Problems 43 vii
Vlll Contents 4 Phase Transitions 47 4.1 First-Order Phase Transition 47 4.2 Condition for Phase Coexistence 49 4.3 Clapeyron Equation 50 4.4 Van der Waals Equation of State 51 4.5 Virial Expansion 53 4.6 Critical Point 53 4.7 Maxwell Construction 55 4.8 Scaling 56 4.9 Nucleation and Spinodal Decomposition 57 Problems 60 References 63 5 The Statistical Approach 65 5.1 The Atomic View 65 5.2 Random Walk 67 5.3 Phase Space 69 5.4 Distribution Function 70 5.5 Ergodic Hypothesis 72 5.6 Statistical Ensemble 72 5.7 Microcanonical Ensemble 73 5.8 Correct Boltzmann Counting 74 5.9 Distribution Entropy: Boltzmann's H 76 5.10 The Most Probable Distribution 77 5.11 Information Theory: Shannon Entropy 78 Problems 80 References 82 6 Maxwell-Boltzmann Distribution 83 6.1 Determining the Parameters 83 6.2 Pressure of Ideal Gas 84 6.3 Equipartition of Energy 85 6.4 Distribution of Speed 87 6.5 Entropy 88 6.6 Derivation of Thermodynamics 89 6.7 Fluctuations 90 6.8 The Boltzmann Factor 91 6.9 Time's Arrow 92 Problems 93 References 97 7 Transport Phenomena 99 7.1 Collisionless and Hydrodynamic Regimes 99 7.2 Maxwell's Demon 101 7.3 Nonviscous Hydrodynamics 101
Contents ix 7.4 Sound Wave 103 7.5 Diffusion 103 7.6 Heat Conduction 105 7.7 Viscosity 106 7.8 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 114 8.4 Connection with Thermodynamics 114 8.5 Energy Fluctuations 115 8.6 Minimization of Free Energy 116 8.7 Classical Ideal Gas 118 Problems 119 9 Grand Canonical Ensemble 123 9.1 The Particle Reservoir 123 9.2 Grand Partition Function 123 9.3 Number Fluctuations 124 9.4 Connection with Thermodynamics 125 9.5 Parametric Equation of State and Virial Expansion 126 9.6 Critical Fluctuations 127 9.7 Pair Creation 128 Problems 130 10 Noise 133 10.1 Thermal Fluctuations 133 10.2 Nyquist Noise 134 10.3 Brownian Motion 136 10.4 Einstein's Theory 138 10.5 Diffusion 140 10.6 Einstein's Relation 142 10.7 Molecular Reality 143 10.8 Fluctuation and Dissipation 144 10.9 Brownian Motion of the Stock Market 145 Problems 148 References 149 11 Stochastic Processes 151 11.1 Randomness and Probability 151 11.2 Binomial Distribution 152 11.3 Poisson Distribution 154
X Contents 11.4 Gaussian Distribution 155 11.5 Central Limit Theorem 157 11.6 Shot Noise 157 Problems 160 References 162 12 Time-Series Analysis 163 12.1 Ensemble of Paths 163 12.2 Ensemble Average 164 12.3 Power Spectrum and Correlation Function 165 12.4 Signal and Noise 168 12.5 Transition Probabilities 170 12.6 Markov Process 171 12.7 Fokker-Planck Equation 172 12.8 The Monte Carlo Method 173 12.9 Simulation of the Ising Model 176 Problems 179 References 181 13 The Langevin Equation 183 13.1 The Equation and Solution 183 13.2 Energy Balance 185 13.3 Fluctuation-Dissipation Theorem 187 13.4 Diffusion Coefficient and Einstein's Relation 187 13.5 Transition Probability: Fokker-Planck Equation 188 13.6 Heating by Stirring: Forced Oscillator in Medium 189 Problems 192 14 Quantum Statistics 195 14.1 Thermal Wavelength 195 14.2 Identical Particles 197 14.3 Occupation Numbers 198 14.4 Spin 200 14.5 Microcanonical Ensemble 201 14.6 Fermi Statistics 202 14.7 Bose Statistics 203 14.8 Determining the Parameters 204 14.9 Pressure 205 14.10 Entropy 206 14.11 Free Energy 207 14.12 Equation of State 207 14.13 Classical Limit 208 Problems 210 Reference 212
Contents xi 15 Quantum Ensembles 213 15.1 Incoherent Superposition of States 213 15.2 Density Matrix 214 15.3 Canonical Ensemble (Quantum-Mechanical) 216 15.4 Grand Canonical Ensemble (Quantum-Mechanical) 217 15.5 Occupation Number Fluctuations 219 15.6 Photon Bunching 220 Problems 221 References 223 16 The Fermi Gas 225 16.1 Fermi Energy 225 16.2 Ground State 226 16.3 Fermi Temperature 227 16.4 Low-Temperature Properties 228 16.5 Particles and Holes 230 16.6 Electrons in Solids 231 16.7 Semiconductors 233 Problems 235 17 The Bose Gas 237 17.1 Photons 237 17.2 Bose Enhancement 239 17.3 Phonons 241 17.4 Debye Specific Heat 243 17.5 Electronic Specific Heat 244 17.6 Conservation of Particle Number 245 Problems 246 References 249 18 Bose-Einstein Condensation 251 18.1 Macroscopic Occupation 251 18.2 The Condensate 253 18.3 Equation of State 254 18.4 Specific Heat 256 18.5 How a Phase is Formed 257 18.6 Liquid Helium 259 Problems 260 References 263 19 The Order Parameter 265 19.1 The Essence of Phase Transitions 265 19.2 Ginsburg-Landau Theory 266 19.3 Relation to Microscopic Theory 267 19.4 Functional Integration and Differentiation 268
xii Contents 19.5 Second-Order Phase Transition 270 19.6 Mean-Field Theory 271 19.7 Critical Exponents 273 19.8 The Correlation Length 274 19.9 First-Order Phase Transition 277 19.10 Cahn-Hilliard Equation 278 Problems 278 References 280 20 Superfluidity 281 20.1 Condensate Wave Function 281 20.2 Spontaneous Symmetry Breaking 282 20.3 Mean-Field Theory 284 20.4 Observation of Bose-Einstein Condensation 285 20.5 Quantum Phase Coherence 286 20.6 Superfluid Flow 287 20.7 Phonons: Goldstone Mode 289 Problems 290 References 292 21 Superconductivity 293 21.1 Meissner Effect 293 21.2 Magnetic Flux Quantum 294 21.3 Josephson Junction 296 21.4 DC Josephson Effect 298 21.5 AC Josephson Effect 299 21.6 Time-Dependent Vector Potential 300 21.7 The SQUID 300 21.8 Broken Symmetry 302 Problems 303 References 303 Appendix 305 Index 313