The goal of this course is to introduce the fundamentals of Quantum Statistical Mechanics developed and used to elucidate gas phase and condensed phase behaviour, as well as to establish a microscopic derivation of the postulates of Thermodynamics. Classical results are obtained according to the classical limit of the quantum mechanical expressions. Topics include ensembles, Fermi, Bose and Boltzmann statistics, density matrices, mean field theories, phase transitions, chemical reaction dynamics, time-correlation functions, Monte Carlo simulations and Molecular Dynamics simulations.
The official textbook for this class is:
R1: "Introduction to Modern Statistical Mechanics" by David Chandler (Oxford University Press).
However, the lectures will be heavily complemented with material from other textbooks including:
R2: "Introduction to Statistical Thermodynamics" by T.L. Hill (Addison Wesley),
R3: "Statistical Mechanics" by D. McQuarrie (Harper & Row),
R4: "Fundamentals of Statistical and Thermal Physics" by F. Reif (McGraw Hill),
R5: "Statistical Mechanics" by R. Kubo (Noth-Holland Publishing Company),
R6: "A course in Statistical Mechanics" by H.L. Friedman (Prentice-Hall).
All these references are on reserve at the Kline library (KBT) to allow everyone equal usage.
References to specific pages of the textbooks listed above are indicated in the notes as follows: R1(190) indicates ``for more information see Reference 1, Page 190''.
The lecture notes are online at http://xbeams.chem.yale.edu/ ~batista/vaa/index.html
Furthermore, a useful mathematical reference is R. Shankar, Basic Training in Mathematics. A Fitness Program for Science Students, Plenum Press, New York 1995.
A useful search engine for mathematical and physical concepts can be found at http://scienceworld.wolfram.com/physics/
Lecture notes on quantum mechanics can be found at http://xbeams.chem.yale.edu/~batista/vvv/index.html
Grading
There will be no final exam for this class.
The final grading evaluation is the same for both undergraduate and graduate students:
homework and assignments (20%).
three mid-terms (60%) on 02/18/11, 03/21/11 and 04/06/11.
Homework includes exercises described in the lecture notes and computational assignments. Note that some exercises are inserted in the description of the specific topics to facilitate finding the relevant material in the lecture notes, while other exercises are outlined in problem sets. Exercises inserted in the lecture notes that precede a problem set are due the same date as the problem set. However, students are encouraged to hand in their solutions as soon as they have them ready to avoid homework accumulation. Students are encouraged to read the chapter of the textbook ahead of the lectures and solve the inserted problems while studying the lecture notes. Quizes on random lectures will include either material from previous lectures or general questions about the material to be covered in that specific lecture.
Distribution of Topics
1. Jan. 10 - Feb. 5: The Statistical Method and Ensembles (Chapter 3)
2. Feb. 7 - Feb. 23: Ideal Systems (Chapter 4, and refs)
3. Feb. 25 - Mar. 4: Theory of Phase Transitions (Chapter 5, and refs)
4. Exam 1: February 18.
5. Mar. 7 - 18: Spring Break.
6. Exam 2: March 21.
7. Mar. 21 - Apr. 1: Monte Carlo Methods in Statistical Mechanics (Chapter
6, and refs)
8. Apr. 4 - Apr. 15: Classical Fluids and Solvation
(Chapter 7, and refs)
9. April 6: Exam 3.
10. April 16: Computer assignments deadline.
11. April 18-29: Non-Equilibrium and Molecular Dynamics (Chapter 8 and
refs)
12. April 29, 9:00 am SCL 18 (Optional comprehensive makeup exam).
Contact Information
Office hours will be held at SCL 239, on Tuesday and Thursday from 3:00 pm to 4:00 pm. You can also send me email to victor.batista@yale.edu, or call me at (203) 432-6672 if you have any question.
History of Statistical Mechanics and Thermodynamics.