Lectures: Difference between revisions

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*Example: Landau diamagnetism.
*Example: Landau diamagnetism.
*Example: Stoner ferromagnetism.
*Example: Stoner ferromagnetism.
*Example: White dwarfs, neutron stars and black holes ([http://physics.aps.org/articles/v3/95 Hawking radiation]).
*Example: White dwarfs, neutron stars and black holes ([http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html Heuristic explanation of Hawking radiation];  [http://physics.aps.org/articles/v3/95 Hawking radiation in optical experiments]).
=== Additional references ===
=== Additional references ===
* R. Balian and J.-P. Blaizot, ''Stars and statistical physics: A teaching experience'', Am. J. Phys. '''67''', 1189 (1999). [http://ajp.aapt.org.proxy.nss.udel.edu/resource/1/ajpias/v67/i12/p1189_s1 [PDF]]
* R. Balian and J.-P. Blaizot, ''Stars and statistical physics: A teaching experience'', Am. J. Phys. '''67''', 1189 (1999). [http://ajp.aapt.org.proxy.nss.udel.edu/resource/1/ajpias/v67/i12/p1189_s1 [PDF]]

Revision as of 11:58, 22 March 2011

Lecture 1: Failure of classical statistical mechanics

  • Example: Planck theory of black-body radiation.

Additional references

Lecture 2: Mixed states in quantum mechanics and the density operator

  • Example: Proper mixed states in spintronics.
  • Example: Improper mixed states in decoherence of qubits and von Neumann entropy.
  • Example: Proper mixed states for quantum systems in thermal equilibrium and density matrix for microcanonical, canonical, and grand canonical ensembles via correspondence with classical statistical mechanics.
  • Example: Density matrix and quantum partition function for a single particle in a box in the quantum canonical ensemble.
  • Example: Density matrix and quantum partition function for a linear harmonic oscillator in the quantum canonical ensemble.

Additional references

  • J. K. Gamble and J. F. Lindner, Demystifying decoherence and the master equation of quantum Brownian motion, Am. J. Phys. 77, 244 (2009). [PDF]
  • A. Ekert and P. L. Knight, Entangled quantum systems and the Schmidt decomposition, Am. J. Phys. 63, 415 (1995). [PDF]

Lecture 3: Many-particle wave functions and the Hilbert space of identical particles

  • Example: Wave functions of 3 fermions and 3 bosons.

Lecture 4: Quantum partition function for many-particle systems in equilibrium

  • Example: Quantum partition function for two bosons and two fermions and comparison with classical statistical mechanics.
  • Example: "Effective force" between noninteracting bosons and fermions due to Pauli principle.
  • Quantum partition function for non-interacting bosons and fermions in the grand canonical ensemble.
  • Example: Equation of state for non-degenerate bosons and fermions.

Additional references

  • W. J. Mullin and G. Blaylock, Quantum statistics: Is there an effective fermion repulsion or boson attraction?, Am. J. Phys. 71, 1223 (2003). [PDF]
  • G. Cook and R. H. Dickerson, Understanding the chemical potential, Am. J. Phys. 63, 737 (1995). [PDF]

Lecture 5: Degenerate fermions in equilibrium

Additional references

Lecture 6: Degenerate bosons in equilibrium

  • Example: Bose-Einstein Condensation for free noninteracting bosons.
  • Example: Bose-Einstein Condensation in dilute trapped atomic gases.
  • The concept of off-diagonal long-range order in the density matrix of Bose-Einstein condensates.
  • Example: Heat capacity of phonons in solids.
  • Example: Magnons in the Heisenberg model of magnetism.

Additional references

  • G. Scharf, On Bose–Einstein condensation, Am. J. Phys. 61, 843 (1993). [PDF]
  • W. J. Mullin, The loop-gas approach to Bose–Einstein condensation for trapped particles, Am. J. Phys. 68, 120 (2000). [PDF]
  • K. Burnett, M. Edwards, and C. W. Clark, The theory of Bose-Einstein condensation of diluted gases, Phys. Today 52(12), 37 (1999). [PDF]

Lecture 7: Magnetic systems

  • Example: Noninteracting spins.
  • Thermodynamics of magnetism.
  • Example: Partition function of the Ising model in one-dimension in an external magnetic field.
  • Example: Onsager solution and computer simulations of the Ising model in two-dimensions.

Lecture 8: Abrupt vs. continuous phase transitions

  • Example: Phase diagrams of liquid-gas and paramagnet-ferromagnet systems.
  • Thermodynamic equation of state near phase transitions.

Lecture 9: Mean-field theory of phase transitions

  • Example: Mean-field theory of the Ising model of magnetism.
  • Example: Mean-field theory of the Heisenberg model of magnetism and upper critical dimensionality.
  • Example: Landau theory and the origin of its failure for two-dimensional Ising model.

Lecture 10: Critical phenomena and renormalization group (RG)

  • Universality and scaling relations
  • Example: Percolation as geometrical phase transition.
  • Example: RG for percolation.
  • Example: RG for 1D Ising model.
  • Example: Niemeijer-van Leeuwen RG in real space for 2D Ising model.

Additional references

  • M. E. Fisher, Renormalization group theory: Its basis and formulation in statistical physics, Rev. Mod. Phys. 70, 653 (1998). [PDF]

Lecture 11: Boltzmann (semiclassical) theory of linear response

  • Example: Conductivity of massless Dirac fermions in 2D graphene.

Lecture 12: Kubo (quantum) theory of linear response

  • Example: Conductivity of electrons in metals.

Lecture 13: Bogoliubov theory of superfluidity

  • Off-diagonal long range order.

Lecture 14: Introduction to quantum phase transitions

  • PDF

Additional references

  • S. Sachdev and B. Keimer, Quantum criticality, Physics Today 64(2), 29 (2011). [PDF]