Spring 2024: Equilibrium Statistical Mechanics

Physics 210A 

Time/Location: M W 9:30 – 10:50am; Mayer Hall Addition 5623
F 2-2:50pm (extra lecture as needed); MHA 5623
TA Discussion session: M 4-4:50pm; MHA 5623
Lecturer: Prof. Terry Hwa
phone: 4-7263; e-mail: 
TA: Brian Vermilyea
Office Hours: instructor (Urey 7222):  Tuesday 2:30-3:30pm
or by appointment [no email consultation on HW the day before due]
TA (MHA 5651): Monday: 5-6pm; Thursday: 2-3pm
Course URL: this page (https://matisse.ucsd.edu/s24-stat-mech/)
Grade 4 problem sets (40%); in-class mid-term (10%), and in-class final (50%).
Scheduled final time: 8-11am, Wednesday 6/12
Prerequisite: undergraduate thermodynamics and statistical mechanics; or equivalent.

Course outline

  • Introduction; review of thermodynamics and entropy
  • Classical ensemble theory and applications
  • Quantum statistical mechanics
  • Statistical mechanics of interacting systems
  • Phase transition and critical phenomena

Reference Books:

There are many textbooks on this classical subject. You may wish to consult some of the standard textbooks, e.g., those by Pathria, Huang, Landau & Lifshitz for classical and quantum stat mech, and the book by Kardar for phase transition and critical phenomena.

Course schedule (tentative):

  Date Topics assignment
L1 Mon, Apr 1 Intro to stat mech; review of thermodynamics and entropy [note] HW1 due Mon Apr 15
  Wed, Apr 3  no class  
L2 Mon, Apr 8 thermodynamic relations and potentials; microcanonical ensemble [note]
L3 Wed, Apr 10
entropy and density of states; partition function [note]
L4 Fri, Apr 12
partition function and Legendre transform; Helmholz free energy [note]
L5 Mon, Apr 15
canonical ensemble and partition function [note] HW1 soln
L6 Wed, Apr 17
maximal entropy principle; simple applications of canonical ensemble [note] HW2 due
Wed May 1 (before class)
L7 Mon, Apr 22
paramagnetism; intro to theory of polymer: entropic elasticity [note
Mon, Apr 22
TA discussion: review HW #1; help on HW#2
L8 Wed, Apr 24
mapping to path integral; confinement cost & delocalization; excluded-volume interaction [note]
L9 Mon, Apr 29
polymer scaling theory; Grand canonical ensemble [note] practice problems
  Mon, Apr 29
TA discussion: HW #2 soln to practice problems 
  Wed, May 1 TA review session (HW2 & practice problems)
  Fri, May 3
(2-2:50 pm)
in-class mid-term (test starts promptly at 2pm; you can bring 2 pages of notes hand-written by you) midterm soln
L10 Mon, May 6 Grand canonical ensemble; equation of state; chemical equilibrium [note] [video] HW2 soln
L11 Wed, May 8 Quantum Stat Mech: quantum many-body state; quantum distribution functions [note] HW3 due Fri May 24
L12 Mon, May 13
weak degeneracy; Virial expansion; strong degeneracy; Sommerfeld expansion [note]
L13 Wed, May 15
degenerate electron gas:  Fermi energy; pressure and specific heat at low temp [note]
L14 Fri, May 17
degenerate Bose gas: Bose-Einstein condensation; thermodynamic properties of Bose gas [note]
L15 Mon, May 20
interacting classical gas: van der Waals eqn of state; liquid-gas transition [note]
L16 Wed, May 22
Intro to ferromagentism; Ising model; Weiss mean-field theory [note]
L17 Fri, May 24
mixing entropy and Bragg-Williams MFT [note]
HW4 due Fri Jun 7
  Mon, May 27 No class (Memorial Day) HW3 soln
L18 Wed, May 29
variational mean-field theory; Potts model  
L19 Mon, Jun 3
spatial correlation in the mean-field approximation  
L20 Wed, Jun 5
validity of mean-field theory; Ginzburg’s  criterion;