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PHYS 813: Quantum Statistical Mechanics
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Course Topics

This is the second core course in the sequence (PHYS 616 + PHYS 813) aimed to introduce physics graduate students to basic concepts and tools of statistical physics. PHYS 616, or equivalent taken at some other institution, is prerequisite to enroll in this course.

Quantum statistical mechanics governs most of condensed matter physics (metals, semiconductors, glasses, ...) and parts of molecular physics and astrophysics (white dwarfs, neutron stars). It spawned the origin of quantum mechanics (Planck's theory of the black-body radiation spectrum) and provides framework for our understanding of other exotic quantum phenomena (Bose-Einstein condensation, superfluids, and superconductors).

The course will focus on practical introduction to QSM via examples and hands-on tutorials using computer algebra system such as Mathematica. The examples will be drawn from the application of QSM to condensed matter physics, phase transitions in magnetic systems, astrophysics, and plasma physics, as are the areas of relevance to research in DPA.

Main Course Topics:

  • proper and improper mixed states in quantum mechanics and the density operator,
  • entanglement and decoherence in quantum mechanics,
  • equilibrium partition function for noninteracting bosons and fermions,
  • electrons in solids,
  • stellar astrophysics,
  • Bose-Einstein condensation in cold atomic gases,
  • phase transitions and critical phenomena (with emphasis on magnetic systems),
  • mean field theory vs. renormalization group methods,
  • quantum phase transitions,
  • elements of nonequilibrium statistical physics: Boltzmann equation, Kubo formula and quantum master equations.


Lecture in Progress

  • Lecture 9: Renormalization group (RG)

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Course Motto

  • In teaching, writing, and research, there is no greater clarifier than a well-chosen example.
  • Formalism should not be introduced for its own sake, but only when it is needed for some particular problem.
  • Physics comes in two parts: the precise mathematical formulation of the laws, and the conceptual interpretation of the mathematics. However, if words of conceptual interpretation actually convey the wrong meaning of the mathematics, they must be replaced by more accurate words. (W. J. Mullin)

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