Statistical Mechanics II

Instructor: 張明哲 

Grading: Midterm (if >10人), Homework, Term paper

Required background:

    Quantum mechanics, Statistical mechanics I, Solid state physics

TA: 蔡承叡

Outline:

    We will study two of the most important manybody topics: superconductivity (discovered 1911)

    and quantum Hall effect (discovered 1980). Before doing that, we will introduce the basic formulation

    of second quantization. This course is for students highly motivated to learn these topics.

References:

    General

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

    Superconductor

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

    Quantum Hall effect

    The quantum Hall effect, by A.H. MacDonald

    The quantum Hall effect, by S. Girvin

Topics to be covered:

    General

        Second quantization (2 col, 1 col)

        Mean field (2 col, 1 col)

        Linear response (2col, 1 col))

    BCS theory of superconductor (2col, 1col)

        Cooper pair

        BCS wave function

        Pairing Hamiltonian

    Inhomogeneous superconductor (2 col, 1 col)

        Bogoliubov-de Gennes equation

        Vortex and its bound states

        Non s-wave pairing

    Integer QHE (introduction ppt)
    Fractional QHE
        Laughlin wave function
        Anyon
        Chern-Simon theory

        Composite fermion