Course Syllabus
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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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Interacting electron gas
One dimensional system
Supplemental Materials: Landau Fermi liquid theory
Supplemental Materials: Superconductivity
Supplemental Materials: Superfluidity
Howework assignment
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Last modified: Jan 7, 2010.