PHY214A: Statistical Physics, Winter 2015

PHY214A: Statistical Physics, Winter 2015

Course Announcements:

  • The final and solutions have been posted and your grades are uploaded to EEE. I will transfer them to the Registrar this weekend; you have until noon Friday to contest your grade, should you have concerns. Thank you for a great quarter!

Course Information:

Instructor: Sid Parameswaran, Assistant Professor

310J Rowland Hall, sidp_at_uci.edu

Office Hours: Tuesdays, 3:00 PM-4:30 PM; Wednesdays, 11:00AM-12:00 PM.

Lectures: Tuesday/Thursday 11:00AM - 12:20 PM, PSCB 230.

Final Exam: Tuesday, March 17, 10:30AM - 12:30 PM, PSCB 230.

Overview:

This is the first in a three-course graduate-level sequence on statistical mechanics. Roughly, this quarter we will cover basic thermodynamics, before briefly reviewing probability theory, and then we will go on to examine the kinetic theory of gases; this will lead us to an understanding of Maxwell-Boltzmann statistics and the ideal gas. We will then discuss quantum statistical mechanics of (ideal) Bose and Fermi gases. Other topics we may cover, time permitting, include the basic theory of interacting gases, an understanding of the van der Waals equation of state, and a rudimentary discussion of critical phenomena.

Prerequisites:

As this is a first-year graduate course, it will be mostly self-contained, but you are expected to be familiar with quantum and statistical mechanics and electrodynamics at the level of our own undergraduate courses. If you have not taken these courses, or are taking them concurrently, but still would like to attend the lectures or sign up for the class, please contact me beforehand. As in all courses and particularly advanced ones, you will get as much out of this class as you put in to it - so keep up with the homework and readings!

Textbook(s):

There are many textbooks that purport to cover 'basic statistical mechanics', but many of these are either too long-winded or at too high or low a level to be useful as a graduate text. Luckily, there is an excellent new book by Mehran Kardar (one of the modern masters of the subject): Statistical Physics of Particles. This will be our text for the course. If you plan to study condensed matter, I strongly recommend also purchasing its companion volume, Statistical Physics of Fields.

Other books that are useful and that you might want to have at hand are Thermodynamics by Fermi (an absolute classic!) and Feynman's Statistical Mechanics: A Series of Lectures.

Lecture Notes and Course Outline:

I will post my handwritten notes whenever possible and appropriate, but I suggest that you take notes in class - particularly as this is a graduate course, I hope there will be a fair amount of discussion in 'real time' that you might like to have a record of.

Here is a rough schedule of topics to be covered. Some topics may bleed into subsequent lectures.

Warning: this is subject to change without notice as the class progresses.

I will have to miss the final lecture or two of the course, owing to a conference commitment; I hope to make these up during the quarter and will poll the class on a suitable date for the make-up lecture(s).

Jan. 6: Thermodynamics introduction; state functions; Zeroth and First law of thermodynamics

Jan. 8: Second law of thermodynamics; entropy, Carnot engines.

Jan. 13: Maxwell Relations; Gibbs-Duhem relation; Third law + examples.

Jan. 15: Probability review.

Jan. 20: Finish probability;.

Jan. 22: Kinetic theory of Gases; brief discussion of BBGKY hierarchy, Boltzmann equation, H-theorem

Jan. 27: Continue kinetic theory; start classical statistical mechanics: overview and definitions.

Jan. 29: Continue Classical statistical mechanics

Feb. 3: Microcanonical ensemble; two level systems; the ideal gas

Feb. 5: Canonical ensemble

Feb. 10: More canonical ensemble

Feb. 12: Gibbs/grand canonical ensembles

Feb. 17: Quantum statistical mechanics: overview; rotational and vibrational modes of molecules; vibrations and specific heat of solids.

Feb. 19: Black-body radiation; quantum micro- and macro-states; microcanonical, canonical and Grand canonical formulations

Feb. 24: Indistinguishable particles, and canonical versus grand-canonical treatments

Mar. 26: Ideal quantum gases in the non-degenerate limit

Mar. 3: Degenerate Fermi gas

Mar. 5: Degenerate Bose gas

These notes are organized by topic rather than by the actual lecture; so some span multiple lectures, or vice-versa.

Course Overview

    1. Thermodynamics
  1. Probability
  2. Kinetic Theory
  3. Classical Statistical Mechanics
  4. Quantum Statistical Mechanics
    1. Introduction
    2. Micro- and macro-states
    3. Ideal Quantum Gases - Non-degenerate
    4. Degenerate Fermi gas
    5. Degenerate Bose gas

If you prefer a single large file with all the lectures, here is the combined PDF (warning, 152 pages, file size~20MB).

Problem Sets:

There will be one problem set every week to 10 days; each set will contain 3-4 problems with 1-2 graded at random - so you should attempt all problems.

Problem sets will be due in class. No extensions will be given without prior approval; late submissions will be penalized at the rate of 20% of the total grade per day, with counting beginning at the end of the class in which the set is due.

  1. Problem Set 1, due Thursday, January 15 Friday, January 16, by 4pm.
  2. Problem Set 2, due Thursday, January 22.
  3. Problem Set 3, due Thursday, January 29.
  4. Problem Set 4, due Tuesday, February 10.
  5. Problem Set 5, due Thursday, February 26.
  6. Problem Set 6, due Thursday, March 5.
  7. Problem Set 7, due Thursday, March 12.

[Take-Home Midterm]

[Problem Session]

[Final Exam]

Solutions in PDF form available on request - please email me directly if you require these.

Grading:

Your grade will be based on the problem sets (25%), a mid-term exam (25%) and a final exam (50%). All exams will be in-class and closed book, and no cheat sheets or notes may be used.