Advanced Statistical mechanics (PHYS 80503-01, CRN 20224)

• General Information (Syllabus)

• Lecture 1. Collective excitations in solids: from particles to fields
• Lecture 2. Landau-Ginzburg theory of phase transitions
• Lecture 3. Fluctuations
• Lecture 4. The scaling hypothesis, renormalization group theory
• Lecture 5. Perturbative renormalization group. First order

• From Stat Mech I: Probability theory, basics
• From Stat Mech I: Gibbs-Duhem equation. Phase transitions.
• From Stat Mech I: Equilibrium statistical mechanics, classical ensembles
• From Stat Mech I: Quantum statistical mechanics
• From Stat Mech I: Addendum on quantum statistical ensembles
• From Stat Mech I: Degenerate quantum ideal gases
• From Math Methods in Physics: Eigenvalues, eigenvectors

• Appendix A: The saddle-point method (uses Eq. (30) from Probability theory lecture above).
• Appendix B: Functional integration. Gaussian functional integrals.
• Appendix C: Solving the Cauchy functional equation. (an article)
• Appendix D: A note on the relationship between Bose-Einstein condensation and superfluidity

1. HW1  (due Mon 11:59pm, Oct 27)  

• MIT Open Courseware Statistical Mechanics II: Statistical Physics of Fields by Mehran Kardar
• A review paper on the relationship between Bose-Einstein condensation and superfluidity, by S. I. Vilchynskyy, A. I. Yakimenko, K. O. Isaieva and A. V. Chumachenko, Low Temperature Physics 39:9, 724 (2013).
• For stochastic phenomena: A modern course in statistical physics, 2nd Edition, by Linda Reichl
• Paper by P.W. Anderson: More Is Different, Science 177, 393 (1972)
• An excellent treatment on scattering: Soft-Matter Characterization see Chapter 1.
• A recent historical review of RG: Fifty years of Wilsonian renormalization and counting, Nature Physics 19, 1521 (2023)

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