B25
Course Coordinator: 
Reiko Toriumi
Statistical Mechanics
Description: 

Statistical physics deals with large collections of particles, typically about 1023. Anything big enough to see with our eyes (daily experience) has enough particles in it to qualify as a subject of statistical physics. Within physics, statistical physics is widely used in condensed matter physics, cosmology, and furthermore it shares a lot of techniques with Quantum Field Theory, which successfully describes at least three fundamental forces in nature: the Strong, Weak, and Electromagnetic forces. Many physical systems, as they constitute many degrees of freedom,  exhibit phase transitions which statistical mechanics lets us explore. At the critical point where phase transitions happen, seemingly different systems exhibit the same universal behavior. This is really an observer's dream. Statistical mechanics bridges the microscopic world with the macroscopic world, i.e., makes the connection between one particle and 1023 particles. It is a way to let the different scales talk to each other. Our course will strive to demonstrate the unity of these perspectives.

Aim: 
The course is designed as an introduction to the methods of Statistical Mechanics. Statistical physics is a thrilling intersection of physical and mathematical ideas which can describe experiences ranging from our daily life to very non-daily ones, possibly including quantum gravity.
Course Content: 

We plan to cover the following material from the textbook
- Chap 1: The Statistical Basis of Thermodynamics
- Chap 2: Elements of Ensemble Theory
- Chap 3: The Canonical Ensemble
- Chap 4: The Grand Canonical Ensemble
- Chap 5: Formulation of Quantum Statistics
- Chap 6: The Theory of Simple Gases
- Chap 7: Ideal Bose Systems
- Chap 8: Ideal Fermi Systems
- Chap 9: Statistical Mechanics of Interacting Systems: Cluster Expansions Method
 

The instructor reserves the right to make minor changes in the syllabus, as needed.

Note: homework asignments are due every Wednesday, before the class. There will be no late homework submission accepted, unless it is discussed with the instructor beforehand.

Lecture meets with Toriumi: Wed:10-12 Fri: 10-11
Discussion meets with Toriumi: Mon: 10-11

The exams will be closed book, but you can bring a single sheet of paper on which you can
write what you want to refer to during the exam on both sides.  Note that I will decide how many midterms we will do shortly after we start the course. Depending on the number of midterms, there will be adjustments on the distribution for the weights of each element (i.e., homework and exams).

Expectations: Students are expected to attend every lecture and discussion. Students are responsible for the materials that are covered in lectures. Note that in lectures, we will cover additional materials that are not discussed in the textbooks. Discussion sessions are designed for you to practice solving problems.
One of the important things in your scientific career is good communication. You will have collaborators, peers, students and public for you to communicate your scientific results with. Without you communicating well about your results, your results may well be equal to nothing. Students are therefore expected to practice good communication with the instructor. Your homework, and your exams for example, are ways to communicate with the instructor. Keep in mind that it is not just about showing that you solved the problems, but it is about showing and demonstrating that your work is legitimate. You are expected to work toward this goal.

Course Type: 
Elective
Credits: 
2
Assessment: 
Weekly assignments (40%); midterm exam (30%); final exam or project (30%)
Text Book: 
Statistical Mechanics, by Pathria and Beale (2011) Elsevier
Reference Book: 
An introduction to Thermal Physics, by Schroeder (2000) Addison Wesley
David Tong, online lectures on Statistical Mechanics
Prior Knowledge: 

Students should have knowledge of Classical Mechanics and Quantum Mechanics to advanced undergraduate level.