Lecture Notes
Lecture 21, May 21: Interactions (SCSM)
Lecture 20, Reading: Renormalization gropup
Lecture 19, June 5: Renormalization group
Lecture 18, June 3: Exact solutions, analytical and numerical (Monte Carlo)
Lecture 17, May 29: Correlation ($\xi$)
Removal: The small last paragraph of 17.3 is now removed. There was an error in the argument, while the conclusion for the DMFT was good (just cannot be inferred this way).—11:34AM, May 29, 2014
Lecture 16, May 27: Landau theory of phase transition
Changes: Footnote 1 removed. Footnote 1 (old footnote 2) is rebuffed with details added (Bragg-Williams free energy is derived in it). Footnote 2 refers to footnote 1.—11:34AM, May 28, 2014
Lecture 15, May 22: Phase transitions
Correction: Eq. 15.25, negative sign, removed. (Thanks, PM!)—5:06PM, Jun 11, 2014
Lecture 14, May 20: Bose gas
Addition: A new footnote (2) regarding the symbol $n$.—9:15AM, May 21, 2014
Correction: $z-1 \rightarrow 1-z$ in page 8, in the first part of proof.—7:07PM, May 20, 2014
Lecture 13, May 15: Fermi gas
Lecture 12, May 13: Quantum ideal gas (general)
Addition: A box, and more comments near the end (Eq. 12.50).—7:44AM, May 15, 2014
Lecture 11, May 8: See LN 10. We also discussed a very important qualitative way to quickly re-derive the Debye $T^3$ law (page 3 of this pdf file). We also discussed how the $T^3$ law would change if we had ferromagnetic spin waves ($\omega \propto k^2$, at long wave length). We derived the answer that $C_V \propto T^{3/2}$. For experimental data on ferromagnetic materials (including EuB$_6$, mentioned in class—not a clear-cut case to demonstrate the $T^{3/2}$ law, I think), check the literature: this or this, for example.
Lecture 10, May 6: Photons, Phonons
Addition: A new footnote (7).—10:08AM, May 13, 2014
Corrections: Eq. 10.15, the $\hbar$ factor is dropped. Eqs. 10.24 and 25 are re-written. The previous version of these two equations were not applicable to all particles.—12:37PM, May 09, 2014
Lecture 9, May 1: Quantum statistical mechanics
Addition: Two section numbers in footnote 8.—10:20AM, May 13, 2014
Additions: A box in page 6. Section 9.3.3. Both of these additions were discussed, in one form or another, in lectures. Footnote 20. (Also, an old footnote (footnote 10, I think) is deleted, as it was found to be unnecessary.)—5:14PM, May 12, 2014
Lecture 8, Apr 29: Some examples of semi-classical ensembles
Change: Discussions in page 14 have been simplified a bit, and then a question has been added.—12:55PM, May 01, 2014
Lecture 7, Apr 24: Various ensembles
Addition: Footnote 5, page 7.—9:35AM, Jun 12, 2014
Addition: Added some more comments to item 4 in page 8.—7:26PM, May 01, 2014
Addition: Key notes added after that super-important table in page 7.—12:44PM, May 01, 2014
Change: The symbol change for microstate (from a left-leaning "mu" to a "mu" with a wavy decorator on lower left).—10:36AM, Apr 25, 2014
Lecture 6, Apr 22: The semi-classical statistical mechanics
Change: The symbol change for microstate just like for LN 7.—10:36AM, Apr 25, 2014
Lecture 5, Apr 17: The irreversibility
Lecture 4, Apr 15: Big numbers
Comment: Definition of correlation and covariance (Eq. 4.13) has a new comment below it. Also, the word covariance is mentioned.—10:33AM, May 01, 2014
Change: Bayesian inference is upgraded from footnote to sub-section (page 3).—7:52PM, Apr 10, 2014
Lecture 3, Apr 10: Probability
Corrections: Eq. 3.3: $\langle p(x) \rangle \rightarrow \langle e^{-ikx} \rangle$. Eq. 3.12: missing $\langle x \rangle_c$ put back for the 4th term (thanks DH, for spotting this typo!).—12:53PM, Apr 17, 2014
Correction: Line 2 of Section 3.2.2: $/N \rightarrow /\sqrt{N}$.—11:19AM, Apr 10, 2014
Lecture 2, Apr 8: Entropy and thermodynamic potentials
More changes: Discussion in Section 2.3 is beefed up a bit (new stuff added here and there). In particular, paragraph 3 (a new one) in page 10 is highly recommended for your careful consumption. In Eq. 2.39 and around it, notation change: $T_0, J_0, S_0 \rightarrow T_R, J_R, S_R$ (better coherence with contents of Section 2.3).—10:13AM, Apr 09, 2014
Changes: Lots of little corrections/improvement/clarifications were added in pages 8 through 17. Please, update! Two most important changes: (i) page 8, Gibbs free energy, the $dG$ expression was jumbled--corrected. (ii) on the same page, $\delta$ is now replaced by $d$.—12:34PM, Apr 08, 2014
Lecture 1, Apr 1: Themodynamics
Addition: Some comments are added after Eq. 1.2. Thanks PM, whose question prompted this addition!—11:50AM, Apr 09, 2014
Correction: Page 2, top, “Debye → de Broglie” (Thanks, PM!)—5:06PM, Jun 11, 2014
Addition: Comments on the van der Waals equation of state (pages 7-8).—11:23AM, May 22, 2014