Ph12c: Satistical Mechanics, Spring 2019
Course description: An introduction to statistical mechanics.
Course Information
Instructor: David Simmons-Duffin, Lauritsen 442, (dsd@caltech). Office hours by appointment.
Textbook: Thermal Physics (2nd Edition) by Charles Kittel and Herbert Kroemer
Lecture notes: Lecture notes are available here: Ph 12c 2019 Lecture notes. They are part of this git repository. If you spot a typo or want to suggest a clarification, and you are familiar with git, please submit a pull request.
Other references: Lecture notes for a previous iteration of this course are available at the Ph 12c 2016 website. This year's course will follow the 2016 course relatively closely, at least for the first several lectures. I am also drawing material from David Tong's lectures on statistical physics.
Offered: Spring term, 2019.
Class meetings:
- Tuesday/Thursday 10:30-11:55am in Lauritsen 269
Recitation leaders:
-
Junyu Liu (jliu2@caltech).
- Recitation: Tuesday 7-8pm in Downs Lauritsen 469.
- Office hours: Wednesday 1-2pm in Downs Lauritsen 413.
- Adriano Testa (atesta@caltech).
- Recitation: Monday 3-4pm in East Bridge 114.
- Office hours: Wednesday 7-8pm in Bridge B157.
Graders:
- Zihao Qi (zqi@caltech) — even-numbered problem sets
- Mackenzie Wooten (mwooten@caltech) — odd-numbered problem sets
Grading: Grades will be based on weekly problem sets (50%),
a midterm (20%), and a final exam (30%). The lowest homework grade
during the term will be dropped.
Homework: Problem sets will be posted on this page on
Thursday, and will be due in the Physics 12c inbox in Bridge Annex at
5:00 pm the following Thursday. Graded homework will be returned to
the Physics 12c outbox in Bridge Annex by the following Monday
morning. Solution sets will be posted on this page. Unexcused late
homework will be accepted for half credit up until one week after the
due date; there is no credit if your assignment is more than one week
late. If your homework will be late for a good reason, you may request
an extension before the assignment is due by sending email to that
week’s grader.
Discussing and working in groups on the problem sets is
encouraged. However, the final writeup must be your own. You may use a
symbolic algebra system like Mathematica or Maple, but please indicate
on your problem set if you do so.
Ombudspeople: Ryan White (rpwhite@caltech, Blacker House),
Eric Moreno (emoreno@caltech, Ricketts House). Please send me an email
if you'd like to volunteer as well.
Notes
- April 4, 2019: This song by
Flanders and Swann may help you remember some of the concepts from
today's class. We'll write down the laws of Thermodynamics next week.
- April 4, 2019: Have a look at
this molecular dynamics
simulation for a simulation of thermal contact. Go to "Presets",
select "Hot and Cold", and click "Start".
- April 4, 2019: Updated the homework policy.
- April 6, 2019: Posted recitation times and office hours for Junyu
and Adriano.
- April 10, 2019: Added hint to problem (2g) on problem set 1.
- April 11, 2019: Fixed the “duality” formula in
problem (4c) on problem set 2: Z(pi/y) -> Z(pi^2/y).
- April 12, 2019: Updated the location of Adriano's office hours.
- April 18, 2019: See this xkcd
comic for a plot of the energy density of the CMB as a function of
frequency. The dots represent data from the COBE satellite, and the
curve is the Planck distribution we derived in class.
- April 19, 2019: If you haven't heard of it, definitely read about
the Riemann
zeta function. For a history and some derivations of values of the
zeta function at even integers, see the Basel
problem.
- April 23, 2019: Added link to lecture notes.
- April 30, 2019: Fixed factor of 2 error on problem 2 of problem
set 4.
- May 13, 2019: Fixed missing factor of A_{T/N} in problem 2b on
problem set 5.
- May 24, 2019: Uploaded new version of pset 4 solutions that
include fixes to problems 3b, 4a, 5b, and 5c.
- May 25, 2019: Uploaded new version of pset 7 with some
clarifications. Note that the second half of problem 2 has been
rewritten.
- May 27, 2019: Fixed typos in pset 7: for (2c), you should
integrate the momentum transfer, not equation (8) (which would just
get you the number of bounces in time dt). Also fixed: upper limits on
integrals in problems 3b and 3c, and missing 1/M factor in eq. (25).
- May 28, 2019: If you're looking for ways to procrastinate as we
approach the end of term, you can play
arXiv vs. snarXiv.
- May 28, 2019: You'll be honored to hear that we are the last
class to experience the true horribleness of old Lauritsen 269. The
room is being renovated this summer. Three chair samples are on the
fourth floor of Lauritsen near the blackboards outside room 469. You
can try them out if you like.
- June 7, 2019: For a visualization of the kind of "fractal"
structure that appears at the critical temperature, have a look at
this simulation
of the 2d Ising model. The simulation shows three different
temperatures: T<T_c, T=T_c, and T>T_c. Above and below the
critical temperature, the structure of fluctuations changes with
distance scale. Below T_c, the system looks ordered at long
distances. Above T_c, the system looks completely random
(disordered). Precisely at T=T_c, the system looks the same at all
distance scales.
- June 7, 2019: The final will be a 4.5 hour take-home exam. It
will be released on Monday June 10 and due on Friday June 14 by 8pm in
the Ph 12c inbox.
- June 7, 2019: Problem set 8 solutions have been posted early in
case anyone wants to use them to study. Please don't look at the
solutions if you have an extension on problem set 8.
Homework Assignments
- Problem set 1, due Thursday, April 11 at 5pm.
- Problem set 2, due Thursday, April 18 at 5pm.
- Problem set 3, due Thursday, April 25 at 5pm.
- Problem set 4, due Thursday, May 2 at 5pm.
- Problem set 5, due Thursday, May 16 at 5pm.
- Problem set 6, due Thursday, May 23 at 5pm.
- Problem set 7, due Thursday, May 30 at 5pm.
- Problem set 8, due Thursday, June 6 at 5pm.
Exams
- Midterm, due Friday, May 10 at 8pm.
- Final, due Friday, June 14 at 8pm.
Grades
- Homework: mean 93.7, median 97.6, standard deviation 11.3
- Midterm: mean 72.3, median 79, standard deviation 23.2
- Final: mean 74, median 78, standard deviation 23.5
The total grade was computed via 0.5(Homework) + 0.2(Midterm) + 0.3(final). Letter grades were assigned as follows.
| A+ | 95-100 |
| A | 86-95 |
| A- | 81-86 |
| B+ | 76-81 |
| B | 70-76 |
| B- | 65-70 |
The distribution of grades was: 8 A+, 10 A, 5 A-, 4 B+, 4 B, 5 <= B-.
Please fill out the TQFR for this course if you have not done so. The system will be available until July 7. Have a good summer!