Advanced Condensed Matter Theory


Course Syllabus pdf file

Lecture notes

Formalism: path integrals, operators,
  • Lecture 1 : Path integral for quantum mechanics -- Ref. Altland and Simons Chap 3.2
  • Lecture 2 : Path integral for harmonic oscillators -- Ref. Altland and Simions Chap 3.3.1
  • Lecture 3 : Path integral for double wells, instanton gas -- Ref. Altland and Simons Chap 3.3.2 and 3.3.3, Coleman Chap7.2
  • Supplemental Material : Decay of false vacuum -- Ref. Coleman Chap 7.6
  • Lecture 4 : More applications: dissipative systems -- Ref. Altland and Simons, Chap 3.3.4
  • Lecture 5 : Path integral for quantum spins -- Ref. Altland and Simons, Chap 3.3.5
  • Lecture 6 : Path integral for functional fields and fermions -- Ref. Altland and Simons, Chap 4

    Interacting electron gas
  • Lecture 7 : Perturbation theory for fermions -- Ref. Altland and Simons, Chap 5.2
  • Supplemental Material: Response function
  • Lecture 8 : RPA, Lindhardt Response, Gaussian fluctuations -- Ref. Altland and Simons, Chap 6.2
  • Lecture 9 : Interacting electron gas -- correlation energy
  • Lecture 10 : Interacting electron gas -- life time, Fermi surface
  • Tunneling and Green's function
  • Conductance

    One dimensional system
  • Bethe Ansatz (I) : The BA equations
  • Bethe Ansatz (II) : The ground state and excitations

    Supplemental Materials: Landau Fermi liquid theory
  • Phenomenology (I) : Landau parameters and collective excitations
  • Phenomenology (II) : Boltzman equation, zero sound
  • Microscopic theory (I) : Vertex functions.
  • Microscopic theory (II) : Ward Identities and Luttinger theorem.
  • Microscopic theory (III): More

    Supplemental Materials: Superconductivity
  • Electron-Phonon interaction
  • Phenomenology of superconductivity
  • BCS-mean field theory
  • Thermodynamics, McMillan formula, linear response and coherence factors
  • GL theory, EM response, and dirty superconductor
  • Functional field method to GL equation and EM response
  • Unconventional Superconductivity
  • Phase sensitive detection to Unconventional Superconductivity
  • p-wave, He-3 A and B, d-vectors, topological edge stades

    Supplemental Materials: Superfluidity
  • Mean-field theory for superfluidity
  • Path integral for superfluidity
  • Low dimensional superfluidity
  • Renormalization group theory for K-T transition
  • EM response of charged superfluidity


    Howework assignment

    Final project








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    Last modified: Jan 7, 2010.