**PH-704 Condensed Matter Theory-II**

- Interacting Bosons and superfluidity: Quantum liquids, Bose-Einstein condensation, the macroscopic wave function, superfluid properties of He II, flow quantization and vortices, quasiparticle excitations, Landau-Ginzburg theory of phase transitions, the macroscopic coherent state, spontaneous symmetry breaking, off-diagonal long range order, macroscopic quantum interference, the weakly interacting Bose gas, Bogoliubov’s theory.
- Conventional superconductivity: Phenomenology, electron-phonon effective interaction, Cooper pairs, pair amplitude, BCS ground state, pair fluctuations, ground state energy, critical magnetic field, energy gap, quasiparticle excitations, thermodynamics, experimental applications, Josephson tunneling.
- Superfluid 3He and unconventional superconductivity: The Fermi liquid normal state of 3He, the pairing interaction in liquid 3He , superfluid phases of 3He, unconventional superconductors.
- Quantum Hall effects: Introduction, Landau levels, the role of disorder, currents at the edge, Laughlin state and its quasiparticles, effective Chern-Simons theory for quantum Hall states.
- Quantum phase transitions: Quantization with path integral methods, the path integral for Bosons, the path integral for Fermions, quantum rotor models, symmetry breaking transition and Mott insulator in a quantum rotor model, scaling, mean field solution.
- The renormalization group: The one-dimensional Ising model, general theory of renormalization group, Berezinskii-Kosterlitz-Thouless transition.

**Recommended texts: **

*Advanced Solid State Physics*, by P. Philips, publisher: Westview Press; 1st edition, (2003).*Condensed Matter Field Theory*, by A. Altland and B. Simons, publisher: Cambridge University Press, 1st edition (2006).*Superconductivityy, Superfluids and Condensates*, by J. F. Annett, publisher: Oxford University Press, 1st edition (2004).