Course syllabus (PDF file)

This the course page for Statistical Mechanics and Chemistry, taught by Prof. Pratyush Tiwary in Spring 2023. Relevant links, references etc. will be uploaded here. I will also upload homework/exam problems here (but likely not their solutions except those for midterms and final exam). The class will taught in-person, with recorded videos through youtube available after class. However you should try your best to attend the live classes and engage in discussions on the slack workspace if you want to make the best of this class.

What's new:

• May 9 Tuesday will be last day of class. No class on May 11 Thursday.

• Final exam (in-class, closed book, closed notes, closed internet, 2-sided 1-page cheat sheet allowed) will be per university schedule on May 13 Saturday, 8-10AM in regular class room.
  
  

Lectures:

Lecture 26 (May 9): Introduction to Renormalization Group. Semester wrap-up.

• Lecture 25 PDF notes, video (youtube link)

Lectures 24, 25 (May 2, 4): Mean field theory for phase transitions. Broken symmetry. Introduction to Renormalization Group.

• Lecture 25 PDF notes, video (youtube link)

• Lecture 24 PDF notes, audio (youtube link - only audio)

• Optional reading: Expository article on Renormalization Group (PDF) by Maris and Kadanoff

Lectures 22, 23 (Apr 25, 27): Van der Waals equation of state from perturbation theory. Ising Models and Peierls droplet argument to phase transitions in 1-d and 2-d Ising model. 

• Check out this web-based Ising model app, courtesy of Prof. John Weeks

• Lecture 23 PDF notes, video (youtube link)

• Lecture 22 PDF notes, video (youtube link)

Lectures 20, 21 (Apr 18, 20): Zwanzig's statistical mechanics perturbation theory. 

• Lecture 21 PDF notes, video (youtube link)

• Lecture 20 PDF notes, video (youtube link)

• Homework 5 (PDF).

Lectures 18, 19 (Apr 11, 13): Interacting systems/classical fluids. Distribution functions. Potential of mean force. 

• Lecture 19 PDF notes, video (youtube link)

• Lecture 18 PDF notes, video (youtube link)

• Extra optional reading on Henderson Theorem (PDF).

Lectures 16, 17 (Apr 4, 6): Free electron model for metals. Photon gas. Blackbody radiation and Planck distribution. 

• Lecture 17 PDF notes, video (youtube link)

• Lecture 16 PDF notes, video (youtube link)

• Extra optional notes on Blackbody radiation (PDF).

• Homeworks 3+4 (PDF).

Lectures 14, 15 (Mar 28, 30): Recap of Phonon gas, Einstein and Debye Models. Recap of Ideal gas of quantum particles: Fermi-Dirac and Bose-Einstein statistics. Bose-Einstein condensation. Classical limits for quantum ideal gases. Free electron model for metals. Photon gas. Blackbody radiation and Planck distribution. Interacting systems/classical fluids. Distribution functions. Potential of mean force. Equation of state for interacting systems.

• Lecture 15 PDF notes, video (youtube link)

• Lecture 14 PDF notes, video (youtube link)

Lectures 11, 12, 13 (Mar 13, 14, 16): Phonon gas: Inability of classical mechanics to explain heat capacity measurements, quantum statistical mechanics to the rescue. Einstein and Debye Models. Ideal gas of quantum particles: Fermi-Dirac and Bose-Einstein statistics. Bose-Einstein condensation. Classical limits for quantum ideal gases. Free electron model for metals. Photon gas. Blackbody radiation and Planck distribution.

• Lecture 13 Old PDF notes from spring 2021 (see page 4-7), old video from spring 2021 (youtube link, start at 24:08)

• Lecture 12 PDF notes, video (youtube link)

• Lecture 11 PDF notes, video (youtube link)

Lecture 10 (Mar 7): Averages and fluctuations from Grand Canonical Ensemble. Gibbs entropy. Introduction to non-interacting ideal systems. 

• Lecture 10 PDF notes, video (youtube link)

Lectures 8-9 (Feb 23, Feb 28): Example using microcanonical and canonical ensemble approaches. Constant chemical potential, volume, temperature (\mu P T) ensemble - Grand Canonical Ensemble. Connections to thermodynamics. Averages and fluctuations from Grand Canonical Ensemble. 

• Lecture 9 PDF notes, video (youtube link)

• Lecture 8 PDF notes, video (youtube link)

Lectures 6-7 (Feb 14, 16 ): Canonical Ensemble: N, V, T as control variables. Canonical Partition Function. Averages and fluctuations from Canonical Partition Function. 

• Read: Expository article by Zia, Redish, McKay showing connection between Legendre and Laplace transforms in thermo and stat mech (PDF)

• Lecture 7 PDF notes, video (youtube link)

• Lecture 6 PDF notes, video (youtube link)

• Homework 2 (PDF file)

Lectures 4-5 (Feb 7, 9 ): Recap: Macrostate, microstate, Ergodicity and the principle of equal a priori probabilities. Microcanonical ensemble: N, V, E as control variables. Microcanonical Partition Function, Boltzmann Entropy and other thermodynamics from Microcanonical ensemble. 

• Lecture 5 PDF notes, video (youtube link)

• Lecture 4 PDF notes, video (youtube link)

Lectures 1-3 (January 26, 31; Feb 2): What is Statistical Mechanics and why study it? Math and Thermo refresher. Introduction to ergodic hypothesis and ensembles. Microcanonical ensemble and the principle of equal a priori probabilities   

• Watch: This Youtube clip (7 min 33 sec)

• Lecture 3 PDF notes, video (youtube link)

• Lecture 2 PDF notes, video (youtube link)

• Lecture 1 PDF notes, video (youtube link)

• Homework1 (PDF file)