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    • 量子系统的非平衡多体理论(英文版)
      • 作者:(意)G.斯蒂芬尼茨//(德)R.冯·莱文
      • 出版社:世界图书出版公司
      • ISBN:9787519264192
      • 出版日期:2019/09/01
      • 页数:600
    • 售价:51.6
  • 内容大纲

        格林函数是解决物理学问题最强大和最通用的方法之一,其中的非平衡态理论对许多研究领域的影响更是不可估量的。本书自成体系,全面论述了非平衡态多体理论。作者从量子力学入手,阐述了平衡态和非平衡态格林函数形式,轮廓格林函数和图解展开式的物理内涵,介绍了这些理论在从分子、纳米结构到金属和绝缘体等诸多领域的应用。本书适用于物理及相关专业的研究生和科研工作者。
  • 作者介绍

  • 目录

    Preface
    List of abbreviations and acronyms
    Fundamental constants and basic relations
    1  Second quantization
        1.1   Quantum mechanics of one particle
        1.2  Quantum mechanics of many particles
        1.3  Quantum mechanics of many identical particles
        1.4   Field operators
        1.5   General basis states
        1.6   Hamiltonian in second quantization
        1.7   Density matrices and quantum averages
    2  Getting familiar with second quantization: model Hamiltonians
        2.1   Model Hamiltonians
        2.2  Pariser-Parr-Pople model
        2.3  Noninteracting models
              2.3.1   Bloch theorem and band structure
              2.3.2   Fano model
        2.4  Hubbard model
              2.4.1   Particle-hole symmetry: application to the Hubbard dimer
        2.5  Heisenberg model
        2.6  BCS model and the exact Richardson solution
        2.7  Holstein model
              2.7.1   Peierls instability
              2.7.2   Lang-Firsov transformation: the heavy polaron
    3  Time-dependent problems and equations of motion
        3.1   Introduction
        3.2  Evolution operator
        3.3  Equations of motion for operators in the Heisenberg picture
        3.4  Continuity equation: paramagnetic and diamagnetic currents
        3.5  Lorentz Force
    4 The contour idea
        4.1   Time-dependent quantum averages
        4.2  Time-dependent ensemble averages
        4.3  Initial equilibrium and adiabatic switching
        4.4  Equations of motion on the contour
        4.5  Operator correlators on the contour
    5    Many-particle Green's functions
        5.1   Martin-Schwinger hierarchy
        5.2  Truncation of the hierarchy
        5.3  Exact solution of the hierarchy from Wick's theorem
        5.4  Finite and zero-temperature formalism from the exact solution
        5.5  Langreth rules
    6  One-particle Green's function
        6.1   What can we learn from G?
              6.1.1    The inevitable emergence of memory
              6.1.2   Matsubara Green's function and initial preparations
              6.1.3   Lesser/greater Green's function: relaxation and quasi-particles
        6.2  Noninteracting Green's function
              6.2.1   Matsubara component
              6.2.2   Lesser and greater components

              6.2.3   All other components and a useful exercise
        6.3  Interacting Green's function and Lehmann representation
              6.3.1   Steady-states, persistent oscillations, initial-state dependence
              6.3.2   Fluctuation-dissipation theorem and other exact properties
              6.3.3   Spectral function and probability interpretation
              6.3.4   Photoemission experiments and interaction effects
        6.4  Total energy from the Galitskii-Migdal formula
    7  Mean field approximations
        7.1   Introduction
        7.2  Hartree approximation
              7.2.1   Hartree equations
              7.2.2   Electron gas
              7.2.3   Quantum discharge of a capacitor
        7.3  Hartree-Fock approximation
              7.3.1   Hartree-Fock equations
              7.3.2   Coulombic electron gas and spin-polarized solutions
    8  Conserving approximations: two-particle Green's function
        8.1   Introduction
        8.2  Conditions on the approximate G2
        8.3  Continuity equation
        8.4  Momentumconservation law
        8.5  Angular momentum conservation law
        8.6  Energy conservation law
    9  Conserving approximations: self-energy
        9.1   Self-energy and Dyson equations I
        9.2  Conditions on the approximate Σ
        9.3  φ functional
        9.4  Kadanoff-Baym equations
        9.5  Fluctuation-dissipation theorem for the self-energy
        9.6  Recovering equilibrium from the Kadanoff-Baym equations
        9.7  Formal solution of the Kadanoff-Baym equations
    10 MBPT for the Green's function
        10.1  Getting started with Feynman diagrams
        10.2  Loop rule
        10.3  Cancellation of disconnected diagrams
        10.4  Summing only the topologically inequivalent diagrams
        10.5  Self-energy and Dyson equations II
        10.6  G-skeleton diagrams
        10.7  W-skeleton diagrams
        10.8  Summary and Feynman rules
    11 MBPT and variational principles for the grand potential
        1l.l   Linked cluster theorem
        11.2  Summing only the topologically inequivalent diagrams
        11.3  How to construct the φ functional
        11.4  Dressed expansion of the grand potential
        11.5  Luttinger-Ward and Klein functionals
        11.6  Luttinger-Ward theorem
        11.7  Relation between the reducible polarizability and the ~ functional
      
    12 MBPT for the two-particle Green's function
        12.1  Diagrams for G2 and loop rule
        12.2  Bethe-Salpeter equation
        12.3  Excitons
        12.4  Diagrammatic proof of K = ±δΣ/δG
        12.5  Vertex function and Hedin equations
    13 Applications of MBPT to equilibrium problems
        13.1  Lifetimes and quasi-particles
        13.2  Fluctuation-dissipation theorem for P and W
        13.3  Correlations in the second-Born approximation
              13.3.1   Polarization effects
        13.4  Ground-state energy and correlation energy
        13.5  GW correlation energy of a Coulombic electron gas
        13.6  T-matrix approximation
              13.6.1   Formation of a Cooper pair
    14 Linear response theory: preliminaries
        14.1  Introduction
        14.2  Shortcomings of the linear response theory
              14.2.1   Discrete-discrete coupling
              14.2.2  Discrete-continuum coupling
              14.2.3  Continuum-continuum coupling
        14.3  Fermi golden rule
        14.4  Kubo formula
    15 Linear response theory: many-body formulation
        15.1  Current and density response function
        15.2  Lehmann representation
              15.2.1   Analytic structure
              15.2.2  The f-sum rule
              15.2.3  Noninteracting fermions
        15.3  Bethe-Salpeter equation from the variation of a conserving G
        15.4  Ward identity and the f-sum rule
        15.5  Time-dependent screening in an electron gas
               15.5.1   Noninteracting density response function
               15.5.2  RPA density response function
               15.5.3  Sudden creation of a localized hole
               15.5.4  Spectral properties in the GoWo approximation
    16 Applications of MBPT to nonequilibrium problems
        16.1  Kadanoff-Baym equations for open systems
        16.2  Time-dependent quantum transport: an exact solution
               16.2.1   Landauer-Büttiker formula
        16.3  Implementation of the Kadanoff-Baym equations
               16.3.1   Time-stepping technique
               16.3.2  Second-Born and GW self-energies
        16.4  Initial-state and history dependence
        16.5  Charge conservation
        16.6  Time-dependent GW approximation in open systems
               16.6.1
        16.8  Response functions from time-propagation
        Appendices
    A From the N roots of ! to the Dirac δ-function
    B Graphical approach to permanents and determinants
    C Density matrices and probability interpretatio
    D Thermodynamics and statistical mechanics
    E Green's functions and lattice symmetry
    F Asymptotic expansions
    G Wick's theorem for general initial states
    H BBGKY hierarchy
    I From δ-like peaks to continuous spectral functions
    J Virial theorem for conserving approximations
    K Momentum distribution and sharpness of the Fermi surface
    L Hedin equations from a generating functional
    M Lippmann-Schwinger equation and cross-section
    N Why the name Random Phase Approximation~
    O Kramers-Kronig relations
    P Algorithm for solving the Kadanoff-Baym equations
    References
    Index

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