PH-704 Condensed Matter Theory-II

  1. 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.
  2. 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.
  3. Superfluid 3He and unconventional superconductivity: The Fermi liquid normal state of 3He, the pairing interaction in liquid 3He , superfluid phases of 3He, unconventional superconductors.
  4. 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.
  5.  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.
  6. The renormalization group: The one-dimensional Ising model, general theory of renormalization group, Berezinskii-Kosterlitz-Thouless transition.


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