Thermodynamics and Statistical Mechanics (Core graduate Course)
![תיבת טקסט: Weekly division
week subject
1 Thermodynamics: Basics, Postulates 0-2, temperature, Entropy.
Ideal gas, Tonks gas
2 Van der Waals. Thermodynamic potentials. Minimax principles.
3 Phase diagrams. Maxwell cosntruction. Gibbs rule. Lattice models.
4 Postulate 3. Liouville theorem. Shannon entropy.
5 Entropy maximization in classical stat. mech. ensembles
6 Equipartition and virial theorems. Applications
7 Quantum stat. mech. Density matrix. Entropy. Lattice models
8 1D, 2D, Bethe lattice phase transitions. Mean field.
9 Quantum ideal gas. High-T for bosons and fermions.
10 Virial exapansion. Application to van der Vaals.
11 Debey-Huckel. Approximate methods. Monte Carlo.
12 Second order phase transitions: Landau theory. Critical exponents.
13 Kadanoff scaling. Real space renormalization. Fixed points.](data:image/png;base64,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)
Detailed program
Week 1: Thermodynamics: Basics, Postulates 0-2, temperature, Entropy. Ideal gas, Tonks gas.
- Variables (intensive, extensive), functions, concepts.
- Reversible & irreversible processes. Postulate 0.
- Postulate 1. Postulate 2. Carnot cycle, efficiency,
- Thermodynamic temperature. Kelvin scale.
- Ideal gas.Entropy. Tonks gas.
Week 2: Van der Waals. Thermodynamic potentials. Minimax principles.
- Water phase diagram. Transitions and critical point.
- Van Der Waals (VDW) gas + law of corresponding states.
- Legendre transforms. Thermodynamics potentials (energy U, enthalpy H, Helmholtz free energy F, Gibbs free energy G, grand potential J), Maxwell relations.
- Max S, min U, minima of F and G
- Stability conditions, Global minimum.
- La Chatelier principle, local minimum.
Week 3: Phase diagrams. Maxwell cosntruction. Gibbs rule. Lattice models.
- VDW gas view via Helmholtz free energy. Maxwell construction.
- VDW gas view via Gibbs free energy. Maxwell construction.
- Latent heat.
- Solid-solid melt diagram (liquidus, solidus, eutectic).
- Liquid mixtures. Definition of: Lattice binary melt vs.
- Lattice gas vs. Ising
- Gibbs phase rule.
- Black body radiation, from classical EM.
- 3rd postulate
Week 4: Postulate 3. Liouville theorem. Shannon entropy.
- 3rd postulate (coninued) C_V->0 for T=0. Meaning of "only one ground state" (examples, FD, BE, Debye phonons)
- 1D harmonic oscillator, and Bohr-Somerfeld quantization:
- demonstration that \Gamma=\int dp dq/h.
- Analytical mechanics, Lagrangian & eqns of motion,
- Canonical variables,Hamiltonian & eqns of motion.
- Poisson brackets, Poincare theorem. All this - just quotations; no proof.
- Phase space; flow in phase space is incompressible.
- Liouville's theorem (just quotation) and Liouville's equation, in form of Poisson brackets, and in form of "mass conservation" law.
- Introduction to Shannon entropy.
Week 5: Entropy maximization in classical stat. mech. ensembles
- Extremum of entropy. Microcanonical. Gibbs paradox.
- Canonical ensemble. Example: Ideal gas, de Broglie wavelenth
- Tonks gas. Ideal polymer (continuum). Ideal lattice polymer.
- p-T ensemble (only definition).
- Grand partition function (only definition). Example: ideal polymer
Week 6: Equipartition and virial theorems. Applications
- Ideal polymer in grand-canonical ensemble compared to canonical ensemble.
- Time dependence of entropy. Coarse-grained entropy.
- Equipartition and virial theorems. Application to quadratic forms.
- Dulong-Petit law.
- From virial theorem to equation of state using the pair correlation function
Week 7: Quantum stat. mech. Density matrix. Entropy. Lattice models
- Concepts in quantum mechanics: bra-ket, orthonormal set, operator.
- Projection operator for a pure state. Quantum average using projection operator. Mixed state. Density operator/matrix.
- Von Neuman-Liouville equation.
- Entropy and density matrix for microcanonical and canonical ensembles.
- Density matrix of single particle in a box.
- Electron spin - quantum treatment, density matrix, partition function, magnetization
- Lattice models: Ising (ferro and anti-ferro), Heisenberg (quantum and classical), XY model.
- Solution of 1D Ising w/free boundaries
Week 8: 1D, 2D, Bethe lattice phase transitions. Mean field.
- Spontaneous symmetry breaking
- Why there is no phase transition if 1D? (free energy argument)
- Transfer matrix for 1D Ising.
- Why 1D argument of no-transition fails in 2D?
- Critical point of 2D Ising: dual lattice, high/low temperature expansions.
- Mean-field (Weiss/Bragg-Williams).
- Brief mention of Bethe-Peiels approximation.
- Description of results of Onsager.
- Recitations: Correlation in Ising w/periodic boundaries
- Potts model
Week 9: Quantum ideal gas. High-T for bosons and fermions.
- Quantum ideal gas, quantum corrections at high-T
- (effective repulsion/attraction) in fermions/bosons
Week 10: Virial exapansion. Application to van der Vaals.
- Virial expansion
- Van der Waals gas from virial expansion
Week 11: Debey-Huckel. Approximate methods. Monte Carlo.
- Debye-Huckel theory
- Approximate methods: Gibbs inequality, Peierls inequality.
- Monte Carlo method
Week 12: Second order phase transitions: Landau theory. Critical exponents.
- Phase transition types, historical remarks,liquid-magnetic analogy
- Landau function, critical exponents \alpha, \beta.
- Exponents \gamma, \delta. Divergence of fluctuations.
- Continuous Landau functional, treatment of fluctuations, Correlation function, exponents \nu and \eta.
- Widom and Rushbrooke relations.
Week 13: Kadanoff scaling. Real space renormalization. Fixed points (IF TIME PERMITS)
- Landau function: (1) failure due to large fluctuations; (2) 1st order transition
- Kadanoff scaling function of free energy.
- Pameter space; example 2D Ising.
- Real space renormalizxation. Fixed points (stable, unstable, mixed)
- Identifying 1/y_1=\nu, \alpha=2-d\nu. Concept of k-space RG, and epsilon-expansion.