Table of contents http://www.loc.gov/catdir/toc/cam021/2001037339.html

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### Summary

### Summary

This reader-friendly introduction to the theory that underlies the many fascinating properties of solids assumes only an elementary knowledge of quantum mechanics. Taylor and Heinonen describe the methods for performing calculations and making predictions of some of the many complex phenomena that occur in solids and quantum liquids. Their book, aimed at advanced undergraduates and beginning graduate students, leads the reader from the fundamental behavior of electrons and atoms in solids to the most recently explored manifestations of the quantum nature of condensed matter.

### Reviews 1

### Choice Review

Taylor (Case Western Reserve Univ.) and Heinonen (Seagate Technology) have prepared a fine graduate-level introduction to the traditional core of condensed matter physics, the quantum theory of solids. Graduate students will appreciate the clear, concise style and the gentle introduction to topics such as second quantization and the BCS theory of superconductivity. Nevertheless, this is a sophisticated, theoretically oriented book, and students are advised to work their way through it carefully. Experienced condensed matter scientists will appreciate the treatment in later chapters of contemporary topics such as mesoscopic physics and the quantum Hall effect. There is a small but carefully selected annotated bibliography that students will find helpful. Interestingly, this book has very little overlap with P.M. Chaikin and T.C. Lubensky's fine Principles of Condensed Matter Physics (1995), which covers a variety of modern topics in "soft" condensed matter physics. Together, the two books give a good picture of condensed matter theory at the graduate level. Taylor's book is a worthwhile addition for any university with a graduate program in condensed matter physics or related fields. Graduate students through professionals. M. C. Ogilvie Washington University

### Table of Contents

Preface | p. ix |

Chapter 1 Semiclassical introduction | p. 1 |

1.1 Elementary excitations | p. 1 |

1.2 Phonons | p. 4 |

1.3 Solitons | p. 7 |

1.4 Magnons | p. 10 |

1.5 Plasmons | p. 12 |

1.6 Electron quasiparticles | p. 15 |

1.7 The electron--phonon interaction | p. 17 |

1.8 The quantum Hall effect | p. 19 |

Problems | p. 22 |

Chapter 2 Second quantization and the electron gas | p. 26 |

2.1 A single electron | p. 26 |

2.2 Occupation numbers | p. 31 |

2.3 Second quantization for fermions | p. 34 |

2.4 The electron gas and the Hartree--Fock approximation | p. 42 |

2.5 Perturbation theory | p. 50 |

2.6 The density operator | p. 56 |

2.7 The random phase approximation and screening | p. 60 |

2.8 Spin waves in the electron gas | p. 71 |

Problems | p. 75 |

Chapter 3 Boson systems | p. 78 |

3.1 Second quantization for bosons | p. 78 |

3.2 The harmonic oscillator | p. 80 |

3.3 Quantum statistics at finite temperatures | p. 82 |

3.4 Bogoliubov's theory of helium | p. 88 |

3.5 Phonons in one dimension | p. 93 |

3.6 Phonons in three dimensions | p. 99 |

3.7 Acoustic and optical modes | p. 102 |

3.8 Densities of states and the Debye model | p. 104 |

3.9 Phonon interactions | p. 107 |

3.10 Magnetic moments and spin | p. 111 |

3.11 Magnons | p. 117 |

Problems | p. 122 |

Chapter 4 One-electron theory | p. 125 |

4.1 Bloch electrons | p. 125 |

4.2 Metals, insulators, and semiconductors | p. 132 |

4.3 Nearly free electrons | p. 135 |

4.4 Core states and the pseudopotential | p. 143 |

4.5 Exact calculations, relativistic effects, and the structure factor | p. 150 |

4.6 Dynamics of Bloch electrons | p. 160 |

4.7 Scattering by impurities | p. 170 |

4.8 Quasicrystals and glasses | p. 174 |

Problems | p. 179 |

Chapter 5 Density functional theory | p. 182 |

5.1 The Hohenberg--Kohn theorem | p. 182 |

5.2 The Kohn--Sham formulation | p. 187 |

5.3 The local density approximation | p. 191 |

5.4 Electronic structure calculations | p. 195 |

5.5 The Generalized Gradient Approximation | p. 198 |

5.6 More acronyms: TDDFT, CDFT, and EDFT | p. 200 |

Problems | p. 207 |

Chapter 6 Electron--phonon interactions | p. 210 |

6.1 The Frohlich Hamiltonian | p. 210 |

6.2 Phonon frequencies and the Kohn anomaly | p. 213 |

6.3 The Peierls transition | p. 216 |

6.4 Polarons and mass enhancement | p. 219 |

6.5 The attractive interaction between electrons | p. 222 |

6.6 The Nakajima Hamiltonian | p. 226 |

Problems | p. 230 |

Chapter 7 Superconductivity | p. 232 |

7.1 The superconducting state | p. 232 |

7.2 The BCS Hamiltonian | p. 235 |

7.3 The Bogoliubov--Valatin transformation | p. 237 |

7.4 The ground-state wave function and the energy gap | p. 243 |

7.5 The transition temperature | p. 247 |

7.6 Ultrasonic attenuation | p. 252 |

7.7 The Meissner effect | p. 254 |

7.8 Tunneling experiments | p. 258 |

7.9 Flux quantization and the Josephson effect | p. 265 |

7.10 The Ginzburg--Landau equations | p. 271 |

7.11 High-temperature superconductivity | p. 278 |

Problems | p. 282 |

Chapter 8 Semiclassical theory of conductivity in metals | p. 285 |

8.1 The Boltzmann equation | p. 285 |

8.2 Calculating the conductivity of metals | p. 288 |

8.3 Effects in magnetic fields | p. 295 |

8.4 Inelastic scattering and the temperature dependence of resistivity | p. 299 |

8.5 Thermal conductivity in metals | p. 304 |

8.6 Thermoelectric effects | p. 308 |

Problems | p. 313 |

Chapter 9 Mesoscopic physics | p. 315 |

9.1 Conductance quantization in quantum point contacts | p. 315 |

9.2 Multi-terminal devices: the Landauer--Buttiker formalism | p. 324 |

9.3 Noise in two-terminal systems | p. 329 |

9.4 Weak localization | p. 332 |

9.5 Coulomb blockade | p. 336 |

Problems | p. 339 |

Chapter 10 The quantum Hall effect | p. 342 |

10.1 Quantized resistance and dissipationless transport | p. 342 |

10.2 Two-dimensional electron gas and the integer quantum Hall effect | p. 344 |

10.3 Edge states | p. 353 |

10.4 The fractional quantum Hall effect | p. 357 |

10.5 Quasiparticle excitations from the Laughlin state | p. 361 |

10.6 Collective excitations above the Laughlin state | p. 367 |

10.7 Spins | p. 370 |

10.8 Composite fermions | p. 376 |

Problems | p. 380 |

Chapter 11 The Kondo effect and heavy fermions | p. 383 |

11.1 Metals and magnetic impurities | p. 383 |

11.2 The resistance minimum and the Kondo effect | p. 385 |

11.3 Low-temperature limit of the Kondo problem | p. 391 |

11.4 Heavy fermions | p. 397 |

Problems | p. 403 |

Bibliography | p. 405 |

Index | p. 411 |