Diagrammatics: lectures on selected problems in condensed matter theory

Michael V. Sadovskll9812566392, 9789812566393

The introduction of quantum field theory methods has led to a kind of “revolution” in condensed matter theory. This resulted in the increased importance of Feynman diagrams or diagram technique. It has now become imperative for professionals in condensed matter theory to have a thorough knowledge of this method. There are many good books that cover the general aspects of diagrammatic methods. At the same time, there has been a rising need for books that describe calculations and methodical “know how” of specific problems for beginners in graduate and postgraduate courses. This unique collection of lectures addresses this need. The aim of these lectures is to demonstrate the application of the diagram technique to different problems of condensed matter theory. Some of these problems are not “finally” solved. But the development of results from any section of this book may serve as a starting point for a serious theoretical study.

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Table of contents :
Contents……Page 10
Preface……Page 8
1 Introduction……Page 13
1.1 Quasiparticles and Green’s functions……Page 15
1.2 Diagram technique. Dyson equation……Page 23
1.3 Green’s functions at finite temperatures……Page 25
2.1 Diagram rules……Page 29
2.2 Electron gas with Coulomb interaction……Page 30
2.3 Polarization operator of free electron gas at T = 0……Page 34
2.4 Dielectric function of an electron gas……Page 36
2.5 Electron self-energy effective mass and damping of quasiparticles……Page 40
2.6 RKKY-oscillations……Page 44
2.7 Linear response……Page 47
2.8 Microscopic foundations of Landau-Silin theory of Fermi-liquids……Page 56
2.9 Interaction of quasiparticles in Fermi-liquid……Page 62
2.10 Non-Fermi-liquid behavior……Page 79
3.1 Diagram rules……Page 83
3.2 Electron self-energy……Page 87
3.3 Migdal theorem……Page 96
3.4 Self-energy and spectrum of phonons……Page 99
3.5 Plasma model……Page 104
3.6 Phonons and fluctuations……Page 109
4.1 Diagram technique for “impurity” scattering……Page 113
4.2 Single-electron Green’s function……Page 117
4.3 Keldysh model……Page 126
4.4 Conductivity and two-particle Green’s function……Page 133
4.5 Bethe-Salpeter equation “diffuson” and “Cooperon”……Page 142
4.6.1 Quantum corrections to conductivity……Page 152
4.6.1.1 Technical details……Page 154
4.6.1.2 “Poor man” interpretation of quantum corrections……Page 161
4.6.2 Self-Consistent Theory of Localization……Page 164
4.6.2.1 Metallic phase……Page 167
4.6.2.2 Anderson insulator……Page 169
4.6.2.3 Frequency dispersion of the generalized diffusion coefficient……Page 173
4.7 “Triangular” vertex……Page 174
4.8 The role of electron-electron interaction……Page 177
5.1 Cooper instability……Page 189
5.2 Gorkov equations……Page 197
5.3 Superconductivity in disordered metals……Page 213
5.4 Ginzburg-Landau expansion……Page 220
5.5 Superconductors in electromagnetic field……Page 235
6.1 Phonon spectrum instability……Page 253
6.2 Peierls dielectric……Page 265
6.3 Peierls dielectric with impurities……Page 272
6.4 Ginzburg-Landau expansion for Peierls transition……Page 279
6.5 Charge and spin density waves in multi-dimensional systems. Excitonic insulator……Page 282
6.6.1 Fluctuations of Peierls short-range order……Page 291
6.6.2 Electron in a random field of fluctuations……Page 297
6.6.3 Electromagnetic response……Page 310
6.7 Tomonaga-Luttinger model and non Fermi-liquid behavior……Page 333
Appendix A Fermi Surface as Topological Object……Page 345
Appendix B Electron in a Random Field and Feynman Path Integrals……Page 351
Bibliography……Page 357