A QUANTUM APPROACH TO CONDENSED MATTER PHYSICS

By O. JAVAO

CONTENTS CHAPTER SEMICLASSICAL INTRODUCTION 1 1 ELEMENTARY EXCITATIONS 1 2 PHONONS 1 3 SOLITONS 1 4 MAGNONS 1 5 PLASMONS 1 6 ELECTRON QUASIPARTICLES 1 7 THE ELECTRON–PHONON INTERACTION 1 8 THE QUANTUM HALL E?ECT PROBLEMS CHAPTER SECOND QUANTIZATION AND THE ELECTRON GAS 2 1 A SINGLE ELECTRON 2 2 OCCUPATION NUMBERS 2 3 SECOND QUANTIZATION FOR FERMIONS 2 4 THE ELECTRON GAS AND THE HARTREE–FOCK APPROXIMATION 2 5 PERTURBATION THEORY 2 6 THE DENSITY OPERATOR 2 7 THE RANDOM PHASE APPROXIMATION AND SCREENING 2 8 SPIN WAVES IN THE ELECTRON GAS BOSON SYSTEMS 3 1 SECOND QUANTIZATION FOR BOSONS 3 2 THE HARMONIC OSCILLATOR 3 3 QUANTUM STATISTICS AT ?NITE TEMPERATURES 3 4 BOGOLIUBOV’S THEORY OF HELIUM 3 5 PHONONS IN ONE DIMENSION 3 6 PHONONS IN THREE DIMENSIONS 3 7 ACOUSTIC AND OPTICAL MODES 3 8 DENSITIES OF STATES AND THE DEBYE MODEL 3 9 PHONON INTERACTIONS 3 10 MAGNETIC MOMENTS AND SPIN 3 11 MAGNONS ONE-ELECTRON THEORY 4 1 BLOCH ELECTRONS 4 2 METALS, INSULATORS, AND SEMICONDUCTORS 4 3 NEARLY FREE ELECTRONS 4 4 CORE STATES AND THE PSEUDOPOTENTIAL 4 5 EXACT CALCULATIONS, RELATIVISTIC E?ECTS, AND THE STRUCTURE FACTOR 4 6 DYNAMICS OF BLOCH ELECTRONS 4 7 SCATTERING BY IMPURITIES 4 8 QUASICRYSTALS AND GLASSES DENSITY FUNCTIONAL THEORY 5 1 THE HOHENBERG–KOHN THEOREM 5 2 THE KOHN–SHAM FORMULATION 5 3 THE LOCAL DENSITY APPROXIMATION 5 4 ELECTRONIC STRUCTURE CALCULATIONS 5 5 THE GENERALIZED GRADIENT APPROXIMATION 5 6 MORE ACRONYMS: TDDFT, CDFT, AND EDFT ELECTRON–PHONON INTERACTIONS 6 1 THE FRO¨ HLICH HAMILTONIAN 6 2 PHONON FREQUENCIES AND THE KOHN ANOMALY 6 3 THE PEIERLS TRANSITION 6 4 POLARONS AND MASS ENHANCEMENT 6 5 THE ATTRACTIVE INTERACTION BETWEEN ELECTRONS 6 6 THE NAKAJIMA HAMILTONIAN SUPERCONDUCTIVITY 7 1 THE SUPERCONDUCTING STATE 7 2 THE BCS HAMILTONIAN 7 3 THE BOGOLIUBOV–VALATIN TRANSFORMATION 7 4 THE GROUND-STATE WAVE FUNCTION AND THE ENERGY GAP 7 5 THE TRANSITION TEMPERATURE 7 6 ULTRASONIC ATTENUATION 7 7 THE MEISSNER E?ECT 7 8 TUNNELING EXPERIMENTS 7 9 FLUX QUANTIZATION AND THE JOSEPHSON E?ECT 7 10 THE GINZBURG–LANDAU EQUATIONS 7 11 HIGH-TEMPERATURE SUPERCONDUCTIVITY SEMICLASSICAL THEORY OF CONDUCTIVITY IN METALS 8 1 THE BOLTZMANN EQUATION 8 2 CALCULATING THE CONDUCTIVITY OF METALS 8 3 E?ECTS IN MAGNETIC ?ELDS 8 4 INELASTIC SCATTERING AND THE TEMPERATURE DEPENDENCE OF RESISTIVITY 8 5 THERMAL CONDUCTIVITY IN METALS 8 6 THERMOELECTRIC E?ECTS MESOSCOPIC PHYSICS 9 1 CONDUCTANCE QUANTIZATION IN QUANTUM POINT CONTACTS 9 2 MULTI-TERMINAL DEVICES: THE LANDAUER–BU¨ TTIKER FORMALISM 9 3 NOISE IN TWO-TERMINAL SYSTEMS 9 4 WEAK LOCALIZATION 9 5 COULOMB BLOCKADE THE QUANTUM HALL E?ECT 10 1 QUANTIZED RESISTANCE AND DISSIPATIONLESS TRANSPORT 10 2 TWO-DIMENSIONAL ELECTRON GAS AND THE INTEGER QUANTUM HALL E?ECT 10 3 EDGE STATES 10 4 THE FRACTIONAL QUANTUM HALL E?ECT 10 5 QUASIPARTICLE EXCITATIONS FROM THE LAUGHLIN STATE 10 6 COLLECTIVE EXCITATIONS ABOVE THE LAUGHLIN STATE 10 7 SPINS 10 8 COMPOSITE FERMIONS THE KONDO E?ECT AND HEAVY FERMIONS 11 1 METALS AND MAGNETIC IMPURITIES 11 2 THE RESISTANCE MINIMUM AND THE KONDO E?ECT 11 3 LOW-TEMPERATURE LIMIT OF THE KONDO PROBLEM 11 4 HEAVY FERMIONS