2022 Statistical Mechanics (I) - PHYS521000
Syllabus for Statistical Mechanics (I) – PHYS521000
fundamentals
Introduction
Thermodynamics as an effective theory
Motivation: Why learn statistical mechanics?
The applications of statistical mechanics
Numerical tools
Basic introduction of python
Basic numerics and plot
Random walk and emergent properties
One dimensional random walk
Drunkard’s walk
Scale invariance and the concept of universality class
The diffusion equation
Basic concepts in probability theory
Statistical Mechanics
Thermodynamics and statistical mechanics
A simple example
Review of thermodynamics
Postulates of statistical mechanics
Phase space and Observables
The fundamental postulate
Liouville’s theorem
Ergodicity
Microcanonical ensemble
Canonical ensemble
Generalized ensemble and grand canonical ensemble
Application of statistical mechanics
Interacting free systems
Oscillators
Phonon and photon
Free Fermions and Bosons
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
Epilogue
repository
open issue
Index
