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Phys 7230 Lectures

Final schedule.

  1. Jan 12. Probability.
  2. Jan 14. Probability and probability density
  3. Jan 16. Classical and Quantum Liouville theorem.
  4. Jan 21. Enthropy and the law of increase of enthropy. Temperature. Pathria 2.1-2.3
  5. Jan 23. Microcanonical Ensemble of Harmonic Oscillators. Enthropy, volume, and pressure.
  6. Jan 26. Ideal Gas. Pathria 1.1-1.4
  7. Jan 28. Ideal Gas – continuation.
  8. Jan 30. Enthalpy, Helmholtz and Gibbs free energy.
  9. Feb 2. Fluctuating particle number and chemical potential. Relationship between derivatives. Method of Jacobians.
  10. Feb 4. Relationship between derivatives. Thermodynamic inequalities. Pathria 3.1-3.8
  11. Feb 6. Thermodynamic inequalities. Pathria 3.1-3.8
  12. Feb 9. Canonical (Gibbs) ensemble. Proof of equivalence to the microcanonical ensemble.
  13. Feb 11. Canonical (Gibbs) ensemble. Partition function and free energy. Simplest examples.
  14. Feb 13. Ideal gas via canonical ensemble. Pathria 6.1-6.5, 4.1-4.3.
  15. Feb 16. Bohr-Sommerfeld (quasiclassical) quantization. Evaluation of the partition function in the quasiclassical regime as an integral. Equipartition theorem.
  16. Feb 18. Multiatomic ideal gas. Evaluation of the partition function for the electronic, vibrational, and rotational degrees of freedom.
  17. Feb 20. Grand canonical emsemble. Application to the ideal gas.
  18. Feb 23. Quantum (low temperature) regime of the ideal gas. Bose-Einstein and Fermi-Dirac distribution.
  19. Feb 25. Density of states. Equation of state for the Fermi and Bose ideal gases.
  20. Feb 27. Deviation of quantum equation of state from that of the classical ideal gas.
  21. Mar 2. Quantum gases in nature.
  22. Mar 4. Bose-Einstein distribution. Bose-Einstein condensation. Pathria 7.1-7.2   
  23. Mar 6. Heat capacity and transition to Bose-Einstein condensation.
  24. Mar 9. Photons. Black body radiation.  
  25. Mar 11. Specific heat of solids. Phonons.
  26. Mar 13. Midterm
  27. Mar 16. Midterm: postmortem
  28. Mar 18. Fermi-Dirac distribution, degenerate Fermi gas. Stability of neutron stars.
  29. Mar 20. Specific heat of the degenerate Fermi gas. Sommerfeld expansion.
    Spring Break
  30. Mar 30. Magnetic susceptibility. Pauli paramagnetism and Landau diamagnetism.
  31. Apr 1. Thermodynamic fluctuations.
  32. Apr 3. Evaluation of Gaussian integrals to compute fluctuations
  33. Apr 6. Spatial correlations of fluctuations. Structure function in an ideal Fermi-Dirac and Bose-Einstein gases. Landau and Lifshitz, sec. 117, pp 354-357.
  34. Apr 8. Correlations in solids.
  35. Apr 10. Absence of the crystaline order below 3 dimensions by the analysis of fluctuations in solids.
  36. Apr 13. First order phase transitions. Clapeyron-Clausius equation.
  37. Apr 15. Second order phase transitions.
  38. Apr 17. Ising model. Landau theory of the second order phase transitions.
  39. Apr 20. Critical exponents.
  40. Apr 22. Brownian motion.
  41. Apr 24. Diffusion equation
  42. Apr 27. Einstein relation
  43. Apr 29. Fluctuation-dissipation theorem.
  44. Mar 1. Review.

 

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