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2022 Statistical Mechanics (I) - PHYS521000
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2022 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
    • The solution of 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
    • Key points to learn from the two example
    • Phonon and photon
    • Free Fermions and Bosons
    • Partition function for free fermions and bosons
  • Phases and phase transitions
    • Phases and phase diagram
    • Ising models and spontaneous symmetry breaking
    • The phase diagram of ferromagnetic Ising model on hypercubic lattice (heuristic arguments)
    • Transfer matrix method
    • Mean-field theory
    • Teaser of the Ginsburg-Landau theory
  • Epilogue
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