Department of Physics
University of Illinois at UrbanaChampaign
Room 2119 Engineering Sciences Laboratory MC704,
1110 West Green Street, Urbana, IL 618013080
Phone: 2173334409
Fax: 2172447704
Email efradkin@illinois.edu
http://webusers.physics.illinois.edu/~efradkin/
Time: 10:30 am11:50 am MW
Place: Rm. 158 Loomis Laboratory
Call Number: 36782
Credit: 1 unit.
Office Hours: Tuesdays 4:00pm5:00pm, Rm 2119 ESB
TA: Mr. Lei Xing,
Address: 4133 ESB
Office Hours: Fridays 2:003:00 pm, 3rd. floor Commons area in ICMT (ESB building) (the office hours will be held by Mr. Michael LeBlanc)
Phone: 7218476
email:
leixing2@illinois.edu
Homeworks
Homework Set No. 1
posted on Sunday January 27, 2013; Due date Monday February 4, 2013, 9:00 am
Solutions to Homework Set No. 1
Homework Set No. 2
posted on Friday February 1, 2013; Due date Monday February 18, 2013, 9:00 am
Solutions to Homework Set No. 2
Homework set No. 3
posted on Monday February 18, 2013; Due date Monday march 4, 2013, 9:00 am
Solutions to Homework Set No. 3
Homework set No. 4
posted on Tuesday March 5, 2013; Due Saturday March 16, 2013
Solutions to Homework Set No. 4
Homework set No. 5
posted on Monday March 25, 2013 ; Due date Sunday April 7, 2013
Solutions to Homework Set No. 5
Homework set No. 6
posted on Sunday April 7, 2013; Due date Sunday April 28, 2013
Solutions to Homework Set No. 6
Term Paper
Term Papers:
The Final Exam for this class consists of written Term Paper and an Oral Presentation on the
Term Paper on the day of the Final. Students must do both the term paper and the oral
presentation to be able to pass this course. Each student must
choose a term paper subject before Friday April 5, 2013 .
Please
click here to see a list
of suggested Term Papers.
The term papers are due on the day of the Final Exam. Each term paper should be
written in TeX/Latex format and they should be at least 10 pages long in paper format
(draft RevTeX). On
the day of the Final Exam each student registered in this class will give a 15
minute long oral presentation for the benefit of the rest of the class. I will
arrange for the term papers to be printed into a single pdf file so that you can
learn from each other's work.
Final Exam
The Final Exam will take place on May 8, 2013
from 9:00 am to 12:00 pm and from 1:00 pm to 3:00 pm. The exam will be in Rm 190 ESB which is not our usual classroom.
On that date the students will give their Oral
Presentations and we will have a "miniworkshop''. Students must send me by email the pdf file of their term paper no later than
8:00 pm on the daye before the final. I will bring my laptop to the final with all the
files loaded.
Each student
will have 15 minutes for his/her presentation. We will have a one hour lunch break.
Course Plan
Fundamental Principles of Statistical Mechanics.
Classical Statistical Mechanics. Phase space and ergodicity. Distribution functions.
Postulate of equal apriori probabilities. Statistical independence. Liouville's theorem.
Microcanonical Ensemble.
Quantum Statistical Mechanics. The role of the density matrix. Entropy and the law of increase of
the entropy.
Thermodynamics and Statistical Mechanics.
Temperature. Adiabatic Processes. Pressure. Work and Heat.
Functions of State. Thermodynamic potentials. The Nernst Theorem. Systems with a variable number
of particles. Inequalities and thermodynamic stability.
The Gibbs Distribution
The density matrix. The partition function and the free energy. The Maxwell distribution. The
gibbs distribution for quantum mechanical systems. Derivation of Thermodynamics from Statistical
Mechanics.
Classical Ideal Gases and Kinetic Theory
Ideal gases. The Boltzmann distribution. Classical systems.
Real gases and the role of
collisions. Kinetic theory of dilute gases. The H Theorem.Conservation Laws. Hydrodynamics.
Transport and the Boltzmann equation.
Random Walks, Langevin and Fokker Planck Equations
Simple models of stocahstic processes. Random walks and the diffusion equation. Relation with equilibrium statistical distributions.
Density matrices for quantum systems at finite temperatures. Relation with the FokkerPlanck equation.
Path integral picture of the density matrix. Simple approximations to the path integral. Applications to simple quantum systems and to
FokkerPlanck processes.
Classical Gases in Equilibruim
The free enrgy and the equation of state of an ideal classical gas. The law of Equipartition.
Monoatomic and polyatomic gases. Angular momentum and other internal degrees of freedom.
Nonideal gases. The van der Waals equation of state. Mayer expansions and virial expansions.
Quantum Statistical Mechanics
Density Matrix. Oscillators at finite temperature. Path integrals. Variational approximations.
Systems of bosons and fermions. FermiDirac and BoseEinstein distributions. Bose Condensation.
Blackbody radiation. degenerate electron gases. Electrons in magnetic fields. Relativistic
systems.
Statistical Mechanics and Phase Transitions: Spin Systems
Elementary picture of a magnet. Heisenberg and Ising models. Symmetry and the concept of Order
Parameter.
Independent spins. Interacting spin systems.High temperature and low temperature expansions.
Duality transformations in spin systems.
The onedimensional Ising model. Peierls' argument. Continuous symmetries and
the Mermin Wagner Theorem. Spontaneous symmetry breaking.
Mean field theory and phase transitions. CurieWeiss theory and variational approximations.
Elementary theory of Superfluidity and Superconductivity.
Fluctuations and Correlation functions.
First order and continuous phase transitions. LandauGinzburg phenomenological theory of phase
transitions.
The onedimensional Ising model. The Onsager solution to the twodimensional Ising model.
Critical fluctuations. Scale Invariance and Universality. The renormalization group.
Bibliography
M. Kardar, "Statistical Physics of Particles", and "Statistical Physics of Fields", first edition, Cambridge University Press.
L. D. Landau and E. M. Lifshitz, "Statistical Physics, Third Edition Part 1", Course of
Theoretical Physics, Volume 5. Pergamon Press.
Kerson Huang, "Statistical Mechanics", Second Edition, Wiley.
Richard P. Feynman, "Statistical Mechanics, A set of Lectures", Frontiers in Physics , Benjamin
(Perseus Books).
