Advanced Statistical mechanics (PHYS 80503-01, CRN 21653)

• General Information (Syllabus)

• Lecture 1. Collective excitations in solids: from particles to fields (complete)
• Lecture 2. Landau-Ginzburg theory of phase transitions (complete)
• Lecture 3. Fluctuations (complete)
• Lecture 4. The scaling hypothesis, renormalization group theory (complete)
• Lecture 5. Perturbative renormalization group. First order (complete)
• Lecture 6. Perturbative renormalization group. Second order. ε-expansion. (complete)
• Lecture 8. Series expansions. (complete)
• Lecture 9. Stochastic processes, Markov chains, the Master equation (complete)
• Lecture 10. Langevin equations, Brownian motion, time-dependent Landau-Ginzburg equation (complete)

• From Stat Mech I: Probability theory, basics
• 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 Electrodynamics II: The 4-tensor electromagnetic field
• From Electrodynamics II: Relativistic mechanics and field theory
• From Electrodynamics II: Charged particle in a vector potential
• From Electrodynamics II: Equations of motion of a vector field. Lagrangean 4-density
• From Math Methods in Physics: Eigenvalues, eigenvectors
• From Math Methods in Physics: Tensors

• Appendix A: The saddle-point method (uses Eq. (30) from Probability theory lecture above).
• Appendix B: Functional integration. Gaussian functional integrals. (complete)
• Appendix C: Solving the Cauchy functional equation. (an article)

1. HW1  (due Wed 11:59pm, Sep 20)   Solutions  
2. HW2  (due Wed 11:59pm, Oct 04)   Solutions  

1. Final exam. (due Sat. Dec 16, 11:59PM).  Solutions  

• MIT Open Courseware Statistical Mechanics II: Statistical Physics of Fields by Mehran Kardar
• 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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