Manybody Physics

Instructor:    張明哲 
References:

    General

    Quantum theory of many-particle systems, by Fetter and Walecka

    Many-body quantum theory in condensed matter physics, by Bruus and Flensberg

    Methods of Quantum Field Theory in Statistical Physics, by Abrikosov, Gorkov, and Dzyaloshinski

    Quantum theory of manybody systems, by A.M. Zagoskin

    Quantum theory of the electron liquid, by Giuliani and Vignale

    Many-particle physics, by Mahan

    Superconductor

    Introduction to Superconductivity, 2^nd ed., by Tinkham
    Superconductivity of Metals and Alloys, by de Gennes,

    Theory of Superconductivity, by Schrieffer

Required background:

    complex analysis, Fourier analysis

    quantum mechanics, statistical mechanics, solid state physics
　

Manybody theory is an indispensable tool in studying the fascinating phenomena of superconductor,

superfluid, and other strongly correlated electron systems. In this course, we will study the basic

formulations, and apply them to investigate various types of quantum transport problems.

First semester:

    Second quantization

    Mean field theory

        Hartree-Fock approximation

    Green's function at zero temperature

        Spectral decomposition

        Diagram expansion

        Random phase approximation

    Linear response theory

        Density response and dielectric function

        Current response and conductivity

    Green's function at finite temperature (Matusbara formalism)

        Spectral decomposition

        Diagram expansion

    Disordered system

        Impurity scattering and conductivity

    Non-equilibrium Green's function (Keldysh formalism)

    Quantum kinetic equations
　

    Grading: homeworks

Second semester:

    Electron-phonon coupling

        Phonon Green's function

        Diagram analysis

        Effective electron-electron interaction

    BCS theory of superconductor

        Cooper pair

        BCS wave function

        Pairing Hamiltonian

        Mean-field theory of superconductor

        BCS state as a coherent state

        Spontaneous symmetry breaking of BCS state

        Meissner effect

        Flux quantization

    Inhomogeneous superconductor

        Mean-field Hamiltonian

        Bogoliubov-Valatin transformation

        Bogoliubov-de Gennes equation

        Current carrying state

        Vortex and its bound states

        Andreev reflection

        Tunneling junctions, semiconductor model

        Josephson tunneling

    Nambu-Gorkov formalism

    Non s-wave pairing

    A short lesson on topological insulator

    Grading: term report (oral, written)