Course Syllabus, 531 Statistical Mechanics

Fall Semester 2003

lecturer: Joerg Schmalian,
A-505 Physics, office phone 294 4745, schmalian@ameslab.gov
 
 
 

Week
Date
Lectures/Exams
Homework
Handouts/
Solutions
1
Mon. 
Aug. 25
 THERMODYNAMICS:
Lecture 1: Summary of thermodynamics and the zeroth law: The power of thermodynamics, state variables, equilibrium and temperature

(due Sep. 03) 

  
Wed. 
Aug. 27
 Lecture 2: First and Second  laws of thermodynamics:  Energy conservation, heat flow, entropy changes. 
Fri. 
Aug. 29
 Lecture 3: Third law of thermodynamics and thermodynamic potentials What happens at absolute zero temperature? On the principle of minimal work. Which potential is the right one?
2
Mon. 
Sep. 01
University Holiday

(due Sep. 10) 

  
Wed. 
Sep. 03
 EQUILIBRIUM STATISTICAL MECHANICS, ENSEMBLE THEORY:
Lecture 4: The canonical ensemble, foundation I: The principle of maximum information and entropy. The partition function.
Fri. 
Sep. 05
 Lecture 5: The canonical ensemble, foundation II  Contact to thermodynamics.
3
Mon. 
Sep. 08
 Lecture 6: The canonical ensemble, examples I: Non interacting systems (harmonic oscillators and free spins in a magnetic field)

(due Sep. 17) 
 
Wed. 
Sep. 10
 Lecture 7: The canonical ensemble, examples II: The non-relativistic classical ideal gas, the issue of indistinguishable particles and Gibb's correction factor. 
Fri. 
Sep. 12
 Lecture 8: The canonical ensemble, examples III: The ultra relativistic ideal gas and  the virial theorem.
4
Mon. 
Sep. 15
 Lecture 9: The canonical ensemble, examples IV: The Ising model in one dimension

(due Sep. 24) 

  
Wed. 
Sep. 17
 Lecture 10: The grand canonical ensemble, foundation: Partition function and grand potential
Fri. 
Sep. 19
 Lecture 11: The grand canonical ensemble, ideal quantum gases: The occupation number distribution of ideal Bose and Fermi systems
5
Mon. 
Sep. 22
 Lecture 12: Quantum gases, examples I: The Fermi-gas, specific heat  and paramagnetism
(due Oct. 01) 
  
Wed. 
Sep. 24
 Lecture 13: Quantum gases,  examples II: Bose-Einstein condensation,  4He and trapped atoms
Fri. 
Sep. 26
 Lecture 14: Quantum gases,  examples III:  cont. Bose-Einstein condensation. Can photons condense?
6
Mon. 
Sep. 29
 Lecture 15: Quantum gases,  examples IV: Particle antiparticle mixtures in the relativistic Fermi gas. The hardon-quark gluon plasma transition. 
(due Oct. 08)		  
Wed. 
Oct. 01
 Lecture 16: The micro-canonical ensemble: phase space, entropy  and density of states
Fri. 
Oct. 03
 Lecture 17: The micro-canonical ensemble: one more time the ideal gas
7
Mon. 
Oct. 06
 Lecture 18:  Quantum statistics of mixed states: density matrix, von Neuman equation, subsystems and entropy changes
(due Oct. 15)		  
Wed. 
Oct. 08
 REAL GASES AND PHASE TRANSITIONS:
Lecture 19:  The virial expansion and  van der Waals theory: Low density expansion and the equation of state of the van der Waals theory.
Fri. 
Oct. 10
 Lecture 20: Classification of phase transitions Ehrenfest classification of first and second order phase transitions.
8
Mon. 
Oct. 13
 Lecture 21: The Landau theory of phase transitions: The concept of an order parameter, critical exponents in mean field    
Wed.
Oct. 15
 Lecture 22: Mean field theory: The mean field theory of the Ising model
Fri. 
Oct. 17
 Lecture 23: Scaling close to second order transitions: universality and scaling laws
9
Mon. 
Oct. 20
 Lecture 24: The renormalization group, principle idea:  Renormalization of the one dimensional Ising model and the general idea of flow equations and fixed points  
Wed. 
Oct. 22
 Lecture 25: The renormalization group, a famous example I: Wilson's momentum shell approach
Fri. 
Oct. 24
 Lecture 26: The renormalization group, a famous example II:  Critical exponents close to four dimensions
10
Mon.
Oct. 27
Midterm Exam
 
  
Wed. 
Oct. 29
 Lecture 27:  The Kosterlitz-Thouless transition, I: Vortices, their stability and energy
Fri. 
Oct. 31
 Lecture 28: The Kosterlitz-Thouless transition, II: The renormalization group equation of the transition.
 11
Mon. 
Nov. 03
 Lecture 29: The Kosterlitz-Thouless transition, III: Length scales and the order of the transition    
Wed. 
Nov. 05
 BROWNIAN MOTION AND POLYMER PHYSICS:
Lecture 30: Diffusion: Random walk and Diffusion 
Fri. 
Nov. 07
 Lecture 31:  The fluctuation dissipation theorem: Einstein's approach to noise and response. 
12
Mon. 
Nov. 10
 Lecture 32: Polymer physics: Statistical mechanics of long molecules    
Wed. 
Nov. 12
 Lecture 33:  Polymers and solvents: excluded volume effects, collapse of polymers and relation to the protein folding problem
Fri. 
Nov. 14
 DISORDERED SYSTEMS
Lecture 34: Disordered systems: quenched versus annealed degrees of freedom, the replica trick
 13
Mon. 
Nov. 17
 Lecture 35: Spin glasses: The mean field theory of spin glasses    
Wed. 
Nov. 19
 Lecture 36: Percolation I: introduction and percolation in one dimension.
Fri.
Nov. 21
 Lecture 37: Percolation II: percolation on Caley trees and scaling theory of the transition
14
Mo.-Fr.. 
Nov. 24-28

Thanksgiving Break 
15
Mon. 
Dec. 01
 NON EQUILIBRIUM  STATISTICAL MECHANICS:
Lecture 38: Dynamics close to equilibrium, I: entropy production and generalized currents and forces, example: thermoelectric effects		    
Wed. 
Dec. 03
 Lecture 39:  Dynamics close to equilibrium II: the Boltzmann equation and H-theorem
Fri. 
Dec. 05
 Lecture 40: Dynamics close to equilibrium III: Boltzmann equation: kinetics of  a two component gas
16
Mon.
Dec. 08
 Lecture 41: The fluctuation dissipation theorem II: Response functions and correlation functions and their relationship in quantum systems
 
  
Wed. 
Dec. 10
 Lecture 42: Dynamics far from equilibrium I: nonlinear chemical kinetics 
Fri. 
Dec. 12
 Lecture 43: Dynamics far from equilibrium II: pattern formation in driven systems
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