PHYS 7450 - Advanced Solids State Physics

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Lecture Notes

  • Lecture set 1: Introduction and overview
    • scope and states of condensed matter physics: "More is Different"
    • "standard model" of solid state physics
    • band structure: insulators and conductors
    • experimental probes
  • Lecture set 2: Elasticity, fluctuations and thermodynamics of crystals
    • elasticity of Goldstone modes
    • quantum field theory of lattice vibration: phonons
    • thermodynamics of phonons
    • correlation functions and x-ray scattering
    • Hohenberg-Mermin-Wagner theorem
    • melting
    • elastic nonlinearities and thermal expansion
  • Lecture set 3: Bosonic matter
    • Bose gases thermodynamics and BEC
    • Bogoluibov theory of a superfluid
    • Lee-Huang-Yang thermodynamics
    • Ginzburg-Landau theory and Landau's quantum hydrodynamics
    • XY model, 2d order, vortices and the Kosterlitz-Thouless transition
  • Lecture set 4: Magnetism in charge insulators
    • Paramagnetism
    • Spin exchange vs dipolar interaction
    • Heisenberg model and crystalline anisotropies
    • Mean-field and Landau theory of FM and AFM states
    • Holstein-Primakoff and Schwinger bosons
    • Jordan-Wigner transformation and XXZ chain
    • Coherent-spin states and Berry phases
  • Lecture set 5: Electron liquid
    • electron gas ground state and excitations
    • Fermi gas thermodynamics
    • Pauli magnetism
    • Landau diamagnetism
    • Hartree-Fock theory of interactions
    • Stoner ferromagnetism
    • density response function and screening
    • electron-phonons coupling

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