Superfluidity & Superconductivity

NTopics:

1. Introduction

2. Path integral approach to the quantum partition function (Coherent state path integrals, Expectation values, resolution of identity and trace with coherent states, Fermionic coherent states using Grassmann variables, The partition function, Matsubara frequencies and Matsubara sums , The Green's function, Analytic continuation (including gauged theories)

3. The weakly interacting Bose gas (Mean field theory in the Hamiltonian formalism, The superfluid transition, Low energy effective theory - The XY model, Phase rigidity and dissipationless flow, Quantization of circulation and the vortex solution)

4. Spontaneous symmetry breaking (Nambu-Goldstone theorem, Spontaneous symmetry breaking in a finite system, Off diagonal long range order and coherence)

5. The superconductor as a charged superfluid (The Anderson-Higgs mechanism, The gauged XY model, The penetration depth)

6. The Ginzburg-Landau theory 1 (The GL equations, The coherence length, Two types of SCs, Hc, Hc2 & Hc1)

7. The Ginzburg-Landau theory 2 (The DC and AC Josephson effect, The SQUID)

8. BCS Theory, the microscopic theory of SC (the BCS interaction, the gap equation, Tc, The BCS ground state & condensation energy, the specific heat)

9. Gor'kov's derivation of the Ginzburg-Landau theory starting from BCS theory (the Hubbard-Stratonovich transformation, derivation of GL parameters close to Tc, derivation of the superfluid density and compressibility)

10. Eliashberg theory (The Eliashberg equations, Standard approximations, The Anderson-Morel solution, The Migdal criterion, The importance of the Gor'kov ladder)

11. Special topics

    1. Abrikosov-Gor'kov theory

    2. Topological superconductivity

    3. Superfluid-Superconductor duality

    4. The BKT transition