Fall 2025: M656 Kinetic Theory and Statistical Mechanics
Instructor: Shouhong Wang (5-8350, showang@iu.edu)
Meeting Time: Tuesday-Thursday 12:45 PM–2:00 PM @ Rawles Hall 368
Office Hour:Tuesday-Thursday 3:50 PM–4:50 PM @ Rawles Hall 368
Description:
This is part of a sequence of three courses, taught in three consecutive fall semesters:
- M637: Theory of gravitation
- M655: Mathematical Foundations of Quantum Mechanics
- M656: Kinetic Theory and Statistical Mechanics
These courses will be taught independently to each other, and the students can take any of them in any order. My intention is to offer interested students a first-principle approach and a global mathematical view to theoretical physics, as envisioned by Galileo Galilei, James Clerk Maxwell, Albert Einstein, and Paul Dirac.
In this course, we intend to provide a first-principle approach for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life. We emphasize in particular the symbiotic interplay between statistical physics and advanced mathematics.
We will spend the first half of the semester on fundamentals of statistical physics and the second half on advanced research topics on mathematical theory (PDE, topology, spectral theory, ...) of condensed matter and solid state physics, related to quantum materials.
In particular, the following will hope to be covered:
- Mathematical Principles of Statistical Physics: Guiding principles, Potential-Descending Principle, Dy- namic Law of Physical Motion
- Fundamentals of Thermodynamics
- Statistical Theory of Equilibrium Systems: Quantum mechanics foundations (a crash course of quantum mechanics is provided), Maxwell-Boltzmann distribution, Bose-Einstein distribution, Fermi-Dirac Distribution, Statistical theory of heat
- Thermodynamic phase transitions and fluctuation theory
- Condensates and quantum phase transitions: Quantum mechanism of condensates and superconductivity
- Mathematical theory of the single and twisted bilayer graphene (energy band theory, Bloch-Floquet theory and the topology of flat bands)
There will be no exams. There will be homework sets. We intend to assign some recent research papers for the class to read, hoping this will lead to some research discoveries.
I will distribute some lecture notes, and the following will be consulted
- L. D. Landau & E. M. Lifshitz, Statistical Physics
- Tian Ma & Shouhong Wang, Phase Transition Dynamics, Springer-Verlag, 2nd edition, 2018
- R.K. Pathria, Statistical Mechanics
- Maciej Zworski, Mengxuan Yang, Zhongkai Tao, Mathematical results on the chiral model of twisted bilayer graphene, arXiv:2310.20642