凝聚态物理的格林函数理论 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

凝聚态物理的格林函数理论 英文PDF格式电子书版下载

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Part Ⅰ Green's Functions in Mathematical Physics3

Chapter 1 Time-Independent Green's Functions3

1.1 Formalism3

1.2 Examples8

1.2.1 3-d case9

1.2.2 2-d case10

1.2.3 1-d case11

Chapter 2 Time-dependent Green's Functions13

2.1 First-Order Case of Time-Derivative13

2.2 Second-Order Case of Time-Derivative16

Part Ⅱ One-Body Green's Functions25

Chapter 3 Physical Significance of One-Body Green's Functions25

3.1 One-Body Green's Functions25

3.2 The Free-Particle Case27

3.2.1 3-d case28

3.2.2 2-d case28

3.2.3 1-d case29

Chapter 4 Green's Functions and Perturbation Theory31

4.1 Time-Independent Case31

4.2 Time-Dependent Case36

4.3 Application:Scattering Theory(E>0)40

4.4 Application:Bound States in Shallow Potential Wells(E<0)44

4.4.1 3-d space44

4.4.2 2-d space45

4.4.3 1-d space46

Chapter 5 Green's Functions for Tight-Binding Hamiltonians48

5.1 Tight-Binding Hamiltonians48

5.2 Lattice Green's functions52

5.2.1 1-d simple lattice53

5.2.2 2-d square lattice55

5.2.3 3-d simple cubic lattice58

Chapter 6 Single Impurity Scattering62

6.1 Formalism62

6. 2 Applications69

6.2.1 3-d case69

6.2.2 1-d case73

6.2.3 2-d case75

Chapter 7 Extension Theory for Lattice Green's Functions77

7.1 Introduction77

7.2 Extension of Hamiltonians in Powers79

7.3 Extension of Hamiltonians by Products84

7.4 Extension by Lattice Constructions90

Part Ⅲ Many-Body Green's Functions99

Chapter 8 Field Operators and Three Pictures99

8.1 Field Operators99

8.2 Three Pictures102

8.2.1 Schr？dinger picture102

8.2.2 Heisenberg picture102

8.2.3 Interaction picture103

8.2.4 The relation between interaction and Heisenberg pictures103

Chapter 9 Definition and Properties of Many-Body Green's Functions109

9.1 Definition of the Many-Body Green's Functions109

9.2 The Characteristics and Usage of the Green's Functions116

9.2.1 The Lehmann representation and spectral function116

9.2.2 Evaluation of physical quantities126

9.3 The Physical Significance of the Green's Functions132

9.3.1 Quasiparticles132

9.3.2 Physical interpretation of the Green's function and its poles136

9.4 The Green's functions of Noninteraction Systems141

9.4.1 Fermions(Bosons)141

9.4.2 Phonons143

Chapter 10 The Diagram Technique for Zero-Temperature Green's Functions147

10.1 Wick' Theorem147

10.2 Diagram Rules in Real Space152

10.2.1 Two-body interaction152

10.2.2 External field160

10.2.3 Electron-phonon interaction161

10.3 Diagram Rules in Momentum Space165

10.3.1 Two-body interaction166

10.3.2 External field168

10.3.3 Electron-phonon interaction170

10.4 Proper Self-Energies and Dyson's Equations172

Chapter 11 Definition and Properties of Matsubara Green's Functions183

11.1 The Imaginary-Time Picture183

11.2 The Definition and Properties of the Matsubara Green's Function186

11.2.1 The definition of the Matsubara Green's function186

11.2.2 A significant property of the Matsubara Green's functions187

11.3 The Analytical Continuation and Evaluation of Physical Quantities189

11.3.1 The analytical continuation189

11.3.2 Evaluation of physical quantities193

11.3.3 The Matsubara Green's functions for noninteracting systems194

11.3.4 The formulas for frequency sums195

Chapter 12 Diagram Technique for the Matsubara Green's Functions200

12.1 Wick's Theorem at Finite Temperature200

12.2 Diagram Rules in Real Space205

12.2.1 Two-body interaction206

12.2.2 External field208

12.2.3 Electron-phonon interaction209

12.3 Diagram Rules in Momentum Space211

12.3.1 Two-body interaction213

12.3.2 External field215

12.3.3 Electron-phonon interaction216

12.4 Proper Self-Energies and Dyson's Equations218

12.5 Zero-Temperature Limit220

Chapter 13 Three Approximation Schemes of the Diagram Technique224

13.1 The Formal and Partial Summations of Diagrams224

13.1.1 Formal summations and framework diagrams224

13.1.2 Polarized Green's functions229

13.1.3 Partial summation of diagrams232

13.2 Self-Consistent Hartree-Fock Approximation233

13.2.1 Self-consistent Hartree-Fock approximation method233

13.2.2 Zero temperature236

13.2.3 Finite temperature241

13.3 Ring-Diagram Approximation244

13.3.1 High-density electron gases244

13.3.2 Zero temperature245

13.3.3 Equivalence to random phase approximation262

13.4 Ladder-Diagram Approximation265

13.4.1 Rigid-ball model265

13.4.2 Ladder-diagram approximation268

13.4.3 Physical quantities281

Chapter 14 Linear Response Theory287

14.1 Linear Response Functions287

14.2 Matsubara Linear Response Functions294

14.3 Magnetic Susceptibility297

14.3.1 Magnetic susceptibility expressed by the retarded Green's function297

14.3.2 Magnetic susceptibility of electrons299

14.3.3 Enhancement of magnetic susceptibility300

14.3.4 Dynamic and static susceptibilities of paramagnetic states300

14.3.5 Stoner criterion301

14.4 Thermal Conductivity302

14.5 Linear Response of Generalized Current306

14.5.1 Definitions of several generalized currents306

14.5.2 Linear response307

14.5.3 Response coefficients expressed by correlation functions311

14.5.4 Electric current313

Chapter 15 The Equation of Motion Technique for the Green's Functions317

15.1 The Equation of Motion Technique318

15.1.1 Hartree approximation321

15.1.2 Hartree-Fock approximation322

15.2 Spectral Theorem324

15.2.1 Spectral theorem324

15.2.2 The procedure of solving Green's functions by equation of motion328

15.3 Application:Hubbard Model329

15.3.1 Hubbard Hamiltonian330

15.3.2 Exact solution of Hubbard model in the case of zero bandwidth332

15.3.3 Strong-correlation effect in a narrow energy band335

15.4 Application:Interaction Between Electrons Causes the Enhancement of Magnetic Susceptibility341

15.5 Equation of Motion Method for the Matsubara Green's Functions343

Chapter 16 Magnetic Systems Described by Heisenberg Model348

16.1 Spontaneous Magnetization and Heisenberg Model348

16.1.1 Magnetism of materials348

16.1.2 Heisenberg model350

16.2 One Component of Magnetization For S=1/2 Ferromagnetism354

16.3 One Component of Magnetization for a Ferromagnet With Arbitrary Spin Quantum Number358

16.4 Explanation to the Experimental Laws of Ferromagnets363

16.4.1 Spontaneous magnetization at very low temperature363

16.4.2 Spontaneous magnetization when temperature closes to Curie point364

16.4.3 Magnetic susceptibility of paramagnetic phase365

16.5 One Component of Magnetization for an Antiferromagnet With Arbitrary Spin Quantum Number366

16.5.1 Spin quantum number S=1/2367

16.5.2 Magnetic field is absent372

16.5.3 Arbitrary spin quantum number S373

16.6 One Component of Magnetization for Ferromagnetic and Antiferromagnetic Films374

16.6.1 Ferromagnetic films374

16.6.2 Antiferromagnetic films379

16.7 More Than One Spin in Every Site384

16.7.1 The model Hamiltonian and formalism384

16.7.2 Properties of the system388

16.8 Three Components of Magnetization for a Ferromagnet with Arbitrary Spin Quantum Number401

16.8.1 Single-ion anisotropy along z direction402

16.8.2 Single-ion anisotropy along any direction412

16.8.3 The solution of the ordinary differential equation419

16.9 Three Components of Magnetizations for Antiferromagnets and Magentic Films422

16.9.1 Three components of magnetization for an antiferromagnet422

16.9.2 Three components of magnetization for ferromagnetic films425

16.9.3 Three components of magnetization for antiferromagnetic films439

Chapter 17 The Green's Functions for Boson Systems with Condensation453

17.1 The Properties of Boson Systems with Condensation454

17.1.1 Noninteracting ground state454

17.1.2 Interacting ground state454

17.1.3 The energy spectrum of weakly excited states456

17.2 The Normal and Anomalous Green's functions457

17.2.1 The Green's functions457

17.2.2 The anomalous Green's functions459

17.2.3 The Green's functions for noninteracting systems460

17.3 Diagram Technique462

17.4 Proper Self-Energies and Dyson's Equations469

17.4.1 Dyson's equations469

17.4.2 Solutions of Dyson's equations471

17.4.3 The energy spectrum of weakly excited states473

17.5 Low-Density Bosonic Rigid-Ball Systems476

17.6 Boson Systems at Very Low Temperature481

Chapter 18 Superconductors With Weak Interaction Between Electrons489

18.1 The Hamiltonian490

18.2 The Green's and Matsubara Green's Functions in the Nambu Representation491

18.2.1 Nambu Green's functions491

18.2.2 Nambu Matsubara Green's functions493

18.3 Equations of Motion of Nambu Matsubara Green's functions and Their Solutions494

18.4 Evaluation of Physical Quantities499

18.4.1 The self-consistent equation and the gap function499

18.4.2 Energy gap at zero temperature500

18.4.3 Critical temperature Tc501

18.4.4 Energy gap as a function of temperature△(T)502

18.4.5 Density of states of excitation spectrum502

18.5 Mean-Field Approximation502

18.5.1 Mean-field approximation of the Hamiltonian502

18.5.2 Expressions of the Heisenberg operators504

18.5.3 Construction of the Green's functions506

18.6 Some Remarks508

18.6.1 Strongly coupling Hamiltonian508

18.6.2 The coexistence of superconducting and magnetic states509

18.6.3 Off-diagonal long-range order510

18.6.4 Two-fluid model511

18.6.5 The electromagnetic properties512

18.6.6 High Tc superconductivity513

Chapter 19 Nonequilibrium Green's Functions516

19.1 Definitions and Properties516

19.2 Diagram Technique519

19.3 Proper Self-Energies and Dyson's Equations528

19.4 Langreth Theorem533

Chapter 20 Electronic Transport through a Mesoscopic Structure541

20.1 Model Hamiltonian541

20.1.1 Model Hamiltonian541

20.1.2 Unitary transformation543

20.2 Formula of Electric Current546

20.3 Tunnelling Conductance550

20.4 Magnetoresistance Effect of a FM/I/FM Junction558

Appendix A Wick's Theorem in the Macroscopic Limit568

Appendix B The Hamiltonian of the Jellium Model of an Electron Gas in a Metal571

Appendix C An Alternative Derivation of the Regularity Condition574

Appendix D Identities Valid for Both Trigonometric and Hyperbolic Chebyshev Functions576

Index577