In this post we will see another book in the Advances in Science and Technology in the USSR – Physics series. This one is titled *Quantum Theory of Solids* and was edited by* I. M. Lifshits*.

The present compilation includes four articles on various topics, each of which contains an exposition of the present state of art in the most interesting and timely problems of solid-state theory. The authors are physicists who have contributed significantly to this field of science.

…

It goes without saying that the selection of material to illustrate the achievements in solid-state physics must inevitably be subjective. For the compilation does not hold works on superconductivity, a problem to which a separate book could be devoted. But we still believe that the articles should be of interest to readers who wish to know what is new in solid-state physics.

Out of the four articles three (1, 2, and 4) were translated by Eugene Yankovsky and one (article 3) was translated by E. Kaminskaya. The book was published by Mir Publishers in 1982.

All credits to the original uploader.

DJVU | 9.5 MB | OCR | 320 pages |

You can get the book here.

Password, if needed: *mirtitles*

Contents

Foreword 5

1.

DEFECTS AND SURFACE PHENOMENA IN QUANTUM CRYSTALS

BY A. F. ANDREEV (transl. by E. Yankovsky) 11

1.1 Introduction 11

1.2 Quantum Effects in Crystals 11

1.3 Impurity Quasiparticles: Impuritons 14

1.3.1 Diffusion in an Impuriton Gas 14

1.3.2 Diffusion of Strongly Interacting Impuritons 17

1.3.3 Phonon-Impuriton Interaction 20

1.3.4 One- and Two-Dimensional Impuritons 24

1.4. Vacancies 32

1.4.1 Vacancies in 4He Crystals 32

1.4.2 Zero-Point Vacancies 37

1.4.3 Vacancies in 3He Crystals 40

1.5. Surface Phenomena 42

1.5.1 The Equilibrium Shape of the Crystal-Liquid Interface 42

1.5.2 Crystallization and Melting 48

1.5.3 Crystallization Waves 51

1.6 Faceting Transitions in Crystals 55

1.6.1 The Role of Fluctuations 55

1.6.2 Thermodynamic Relations 58

1.6.3 A 6-fold Symmetry Axis 60

1.6.4 A 4-fold Symmetry Axis 61

1.7 Derealization of Dislocations 64

References 66

2.

ELECTRONIC PHASE TRANSITIONS AND THE PROBLEM OF MIXED VALENCE BY D. I. KHOMSKII

(transl. by E. Yankovsky) 70

2.1 Introduction 70

2.2 Localization of Electrons and Insulator-Metal Transitions (Mott-Hubbard Transitions) 72

2.3 Electronic Phase Transitions in Rare-Earth Compounds 75

2.3.1 The General Picture of Transitions 75

2.3.2 Theoretical Models for Describing Electronic Phase Transitions and MV States 77

2.4 Valence Transitions in the Falicov-Kimball Model 80

2.4.1 The Mean-Field Approximation 80

2.4.2 Beyond the Mean-Field Approximation. The Role of Local (Excitonic) Correlations 84

2.4.3 The Two-Level Model 87

2.4.4 The Periodic Model 89

2.5 The Electron-Lattice Interaction and Its Role in Transitions 91

2.5.1 Interaction with a Homogeneous Strain 91

2.5.2 The Change in the Width of the f Level and Its Role in Valence Transitions 97

2.5.3 Local (Polaron) Effects in the Electron-Lattice Interaction 99

2.5.4 Interaction via Short-Wavelength Phonons and Formation of Ordered Structures 102

2.6 Mixed-Valence States: The Basic Problems 105

2.6.1 Properties of Mixed-Valence States. The Experimental Situation and Statement of the Problem 106

2.6.2 The Anderson and Kondo Lattices 109

2.6.3 The Valence Transition and the Mott-Hubbard Transition 114

2.6.4 Excitonic Correlations in an MV Phase 117

2.6.5 Spatial Correlations in MV Systems 119

2.6.6 Systems with MV as a Model of Condensed Matter 121

2.7 Conclusion 123

References 126

3.

COHERENT EFFECTS IN DISORDERED CONDUCTORS BY

B. L. ALTSHULER, A. G. ARONOV, D. E. KHMELNITSKII

AND A. I. LARKIN (transl. by E. Kaminskaya) 130

3.1 Introduction 130

3.2 Quantum Corrections to Conductivity of Noninteracting Electrons 131

3.2.1 Conductivity and Impurity Diagrammatic Technique 131

3.2.2 Cooperon and Quantum Correction to Conductivity 134

3.2.3 Elects of Spin Scattering 137

3.2.4 Properties of Samples of Finite Dimensions. Effective Space Dimensionality 142

3.3 Quantum Effects in High-Frequency Electromagnetic Field 144

3.3.1 Effects of High-Frequency Field on Quantum Corrections to Conductivity 144

3.3.2 Suppression of Coherent Effects by Electromagnetic Fluctuations 146

3.4 Electron-Electron Interaction in Disordered Metallic Systems 151

3.4.1 Electron-Electron Collision Time 151

3.4.2 Effects of Electron-Electron Correlations on the Density of One-Particle States 160

3.4.3 Conductivity of Interacting Electrons 170

3.4.4 Superconducting Fluctuations and Temperature Dependence of Conductivity 176

3.5 Temperature Dependence of Conductivity: Experiment 179

3.6 Hall Effect 187

3.6.1 Introduction 187

3.6.2 Hall Effect for Noninteracting Electrons 188

3.6.3 Hall Elect for Interacting Electrons 189

3.7 Anomalous Magnetoresistance 191

3.7.1 Magnetoresistance of Noninteracting Electrons 191

3.7.2 Magnetoresistance of Thin Films and Wires in Longitudinal Magnetic Field 194

3.7.3 Magnetoresistance and Scattering by Superconducting Fluctuations 196

3.7.4 Magnetoresistance in Many-Valley Semiconductors 197

3.7.5 Effects of Spin-Orbit Scattering on Magnetoconductivity 199

3.7.6 Experiment 202

3.7.7 Aharonov-Bohm Effect in Disordered Metals 206

3.7.8 Effects of Electron-Electron Interaction in Magnetic Field 208

3.8 Electron Localization in Random Potential 213

3.8.1 Analogy Between Electron Properties in Disordered Systems and Statistical Mechanics of Ferromagnets 213

3.8.2 Q-Hamiltonian 214

3.8.3 Renormalization Group Equation 216

3.8.4 Conductivity in Two Dimensions 217

3.8.5 Localization in One and Three Dimensions 219

3.8.6 Localization in Magnetic Field 222

3.8.7 Localization in Percolating Structures 223

3.9 Conclusion 225

3. A Appendices 226

3.A.1 Cooperon-Current Relation in the Space-Time Representation 226

3.A.2 Cooperon in External Electromagnetic Field 229

3.A.3 Calculation of Path Integrals 230

3.A.4 Expression for Conductivity of Interacting Electrons 232

References 235

4.

AN EXACT SOLUTION OF THE KONDO PROBLEM

BY P.B. WIEGMANN (transl. by E. Yankovsky) 238

4.1 Introduction 238

4.2 The Basic Models 244

4.2.1 The Anderson Model 245

4.2.2 The Angular Dependence of Hybridization Amplitudes. A One-Dimensional Hamiltonian 246

4.2.3 Hierarchy of Energies 247

4.2.4 Exchange Hamiltonians 248

4.2.5 The Simple Exchange Hamiltonians 250

4.2.6 Perturbation Theory 254

4.3 Bethe’s Method 257

4.3.1 General Survey. The Factorization Equations 257

4.3.2 An Effective Hamiltonian 263

4.3.3 The Bethe Ansatz for the s-d Exchange Model 264

4.3.4 Periodic Boundary Conditions 269

4.3.5 The Set of Commuting Operators 269

4.3.6 Diagonalizing T (a) 272

4.3.7 Discussion 275

4.4 The Thermodynamics of the s-d Exchange Model 277

4.4.1 Bethe’s Equations for the s-d Exchange Model. Going Over to the Continuous Limit 277

4.4.2 The Equilibrium Distribution 282

4.4.3 The Free Electron Gas (g -+ 0 or S = 0) 284

4.4.4 Universality 287

4.4.5 The Limits of Strong and Weak Coupling 288

4.4.6 The Thermodynamics of an Impurity 290

4.4.7 Magnetic Susceptibility at 7 = 0 [30, 32, 33] 293

4.4.8 Solution of Equations (4.4.35) and (4.4.36) by an Iterative Method at T > H [36, 38] and Perturbation Theory 297

4.4.9 Supplementary Discussion 300

4.5 Solution for the rc-fold Degenerate Exchange Model 301

4.5.1 The Bethe Ansatz 301

4.5.2 Magnetic Susceptibility at T = 0 303

4.5.3 Thermodynamics 306

4.5.4 Discussion 308

4.6 Conclusion 308

References 311

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