Statistical Mechanics

Syllabus

Main Texts
Other useful texts:
    See the Book List for a list of useful library texts. We will be referring most frequently to Hansen & McDonald or Huang when the primary texts don't contain a topic of interest.
Course Outline
  1. Mathematical Review & Classical Mechanics (McQuarrie, Chapters 1-3 and Chandler, Chapter 3)
    1. Lagrangian Formulation
    2. Hamiltonian Formulation
    3. Poisson Brackets and Canonical Transformations
  2. Classical approach to Ensembles
    1. Ensembles and Phase Space
    2. Liouville's Theorem
    3. Equilibrium Statistical Mechanics and it's ensembles
  3. Elementary Probability Theory
    1. Distributions and Averages
    2. Cumulants and Fluctuations
    3. The Central Limit Theorem
  4. Distributions & Fluctuations (Chandler, Chapter 3)
    1. Theory of Ensembles, Classical and Quantum
    2. Equivalence of Ensembles
    3. Fluctuations of Macroscopic Observables
  5. Basic Thermodynamics (Chandler, Chapter 1)
    1. Review of Concepts
    2. The Laws of Thermodynamics
    3. Legendre Transforms
    4. The Maxwell Relations
    5. The Gibbs-Duhem Equation and Extensive Functions
    6. Intensive Functions
  6. Phases & Phase Transitions: The Ising Model (Chandler, Chapter 5)
    1. Stability of Thermodynamics Phases
    2. First-order Phase transitions
    3. Interfaces
    4. The Ising Model
    5. Lattice Gas
    6. Broken Symmetry
    7. Mean Field Theory
  7. Methodology (Chandler, Chapter 6)
    1. Monte Carlo
    2. Trajectories
    3. Non-Boltzmann Sampling
  8. A brief introduction to Liquid Theory (Chandler, Chapter 7 and McQuarrie, Chapter 13)
    1. Averages
    2. Distribution Functions
    3. Reversible Work Theorem
    4. g(r)
    5. Molecular liquids
  9. Non-equilibrium systems (Chandler, Chapter 8 and McQuarrie Chapters 19-21)
    1. Fluctuation-Dissipation Theorem
    2. Onsager's Regression Hypothesis
    3. Brownian Motion, Friction and the Langevin Equation
    4. Transport
    5. Time Correlation Functions