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Syllabus for Statistical Mechanics (I) – (2024)PHYS521000
fundamentals
Introduction
How to ask a question?
The development of physics
Thermodynamics as an effective theory
Motivation: Why learn statistical mechanics?
The applications of statistical mechanics
Basic concepts in probability theory
Random walk and emergent properties
One dimensional random walk
Drunkard’s walk
The diffusion equation
Guide to Exercise 1
Statistical Mechanics
Thermodynamics and statistical mechanics
A simple example
Review of thermodynamics
Guide to Exercise 2
Postulates of statistical mechanics
Phase space and Observables
The fundamental postulate
Liouville’s theorem
Microcanonical ensemble
Canonical ensemble
Guide to Exercise 3
Generalized ensemble and grand canonical ensemble
Density operator formalism
Ergodicity (Do we really need it?)
Application of statistical mechanics
Other interacting free systems
Oscillators
Guide to Exercise 4
Free Fermions and Bosons
Second quantization
Phonon and photon
Guide to Exercise 5
Phases and phase transitions
Phases and phase diagram
Ising models and spontaneous symmetry breaking
Transfer matrix method
Mean-field theory
Teaser of the Ginsburg-Landau theory
Guide to Exercise 6
Epilogue
Appendix
Exercise
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Numerical tools
Basic introduction of python
Basic numerics and plot
Repository
Open issue
Index
