PHYS 813: Quantum Statistical Mechanics
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Course Topics
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This is the second core course in a sequence (PHYS 616 + PHYS 813) aimed to introduce physics graduate students to basic concepts and tools of statistical physics. Statistical physics is difficult to teach and learn due to:
- students have had little experience making the connection between microscopic and macroscopic phenomena,
- a deep understanding of the probability theory is important,
- the solution of a single equation or a set of equations such as Newton laws, Maxwell equations, or Schrodinger equation is not central to statistical physics, so that there are no standard procedures that work for a large class of problems and many calculations are unfamiliar to students,
- there are few exactly solvable problems.
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:
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- 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.
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News
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- Homework Set 5 has been posted and is due on 05/10.
- Midterm exam is schedule on 04/23 during Tuesday class.
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Lecture in Progress
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- Lecture 5: Phase transitions
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