Core Course on Statistical Mechanics - 2009

This page last updated on 27th May, 2009

Mid-term Test : 10 a.m. - 2 p.m., Saturday 28th March, 2009

Final Test : 10 a.m. - 2 p.m. Saturday 30th May, 2009

The first lecture will be on 2nd February 2009 at 9.45 a.m. in AG 69.

Problem Set 1

Problem Set 2

Evaluation : Assignments : 20 Marks, Mid-term test 40 marks, End-term test 40 marks. Mid term test on Saturday 28th March, 2009 (10 a.m. - 2 p.m.). End-term test on Saturday 30th May, 2009 (10 a.m - 2 p.m.). Both tests will be open book but only the two books by Reif, Huang's book, and Pathria's book, along with your class notes and assignments, can be brought to the test.

Lecture 1.) 2.2.2009 Principles of statistical mechanics. Recall the laws of thermodynamics. Read Chapter 1 of Reif's Berkeley book.

Lecture 2.) 4.2.2009 Principles of statistical mechanics. Read Chapters 2 and 3 of Reif's Berkeley book.

Lecture 3.) 9.2.2009 Thermal Interaction and the canonical ensemble. Read Chapter 4 of Berkeley's book.

Lecture 4.) 11.2.2009 Thermodynamic interaction and conditions for equilibrium. Read Sections 7.1 and 7.2 from Reif's Berkeley book.

Lecture 5.) 16.2.2009 Gibbs free energy and Clausius-Clapeyron equation. Heat engines and refrigerators. Reif (Berkeley) Sections 7.3 onwards, and Reif (Book II) Sections 5.11, 5.12, 8.3 to 8.5

Lecture 6.) 18.2.2009 Liouville's theorem in classical and quantum mechanics. Boltzmann's transport equation. Reif Book II. Another good book for these topics is Tolman's book : Principles of Statistical Mechanics.

Lecture 7.) 23.2.2009 Boltzmann's transport equation and H-theorem. Reference : Huang's book

Lecture 8.) 25.2.2009 Discussion of Boltzmann's H-theorem (Huang's book). The quantum mechanical H-theorem (Reif II).

Lecture 9.) 2.3.2009 Quantum statistics of ideal gas : Distribution functions for Fermi-Dirac and Bose-Einstein statistics (Reif II, Chapter 9)

Lecture 10.) 4.3.2009 Classical statistics of ideal gas and the Gibbs paradox (Reif II)

Lecture 11.) 9.3.2009 Partition function for the quantum ideal gas for various cases and resolution of the Gibbs paradox (Reif II)

Lecture 12.) 16.3.2009 Fermi systems : conduction electrons in metals

Lecture 13.) 18.3.2009 White dwarf stars and the Chandrasekhar mass limit

Lecture 14.) 23.3.2009 Thermodynamics of black holes and other gravitating systems

Lecture 15.) 25.3.2009 Systems of interacting particles : Phonons (Reif Chapter 10)

Lecture 16.) 30.3.2009 Systems of interacting particles: The non-ideal classical gas : derivation of the van der Waals equation of state (Reif Chapter 10.)

Lecture 17.) 1.4.2009 Systems of interacting particles : Ferromagnetism and the Weiss molecular field approximation (Reif Chapter 10)

Lecture 18.) 6.4.2009 Elementary theory of kinetic processes (Reif Chapter 12)

Lecture 19.) 8.4.2009 Path intgral formulation of Boltzmann equation (Reif Chapter 13.)

Lecture 20.) 13.4.2009 Boltzmann equation in the relaxation time approximation and calculation of viscosity and electrical conductivity. (Reif Chapter 13.)

Lecture 21.) 15.4.2009 Near exact formulation of transport theory : the Boltzmann transport equation, an approximate method for its solution, and calculation of viscosity. (Reif Chapter 14.)

Lecture 22.) 20.4.2009 Brownian motion and the Langevin equation (Reif Chapter 15.)

Lecture 23.) 22.4.2009 Brownian motion and the fluctuation-dissipation theorem (Reif Chapter 15.)

Lecture 24.) 27.4.2009 The general fluctuation-dissipation theorem (Reif Chapter 15.)

Lecture 25.) 29.4.2009 The Nyquist theorem (Reif Chapter 15.)

Lecture 26.) 4.5.2009 Phase transformations, critical phenomena and the renormalization group : I. Understanding the existence of the critical point in the gas-liquid phase transition using the van der Waals equation of state (Reif)

Lecture 27.) 6.5.2009 The 1-d Ising model : no spontaneous magnetization (Huang, Plischke and Bergersen)

Lecture 28.) 11.5.2009 The 2-d Ising model and the ferromagnetic phase transition. Critical exponents for the Weiss molecular field theory of the ferromagnetic phase transition. (Huang).

Lecture 29.) 13.5.2009 Critical phenomena : critical exponents, the scaling hypothesis, and scale invariance. (Huang).

Lecture 30.) 18.5.2009 The renormalization group : the 1-d Ising model revisited (Plischke and Bergersen, Huang)

Lecture 31.) 20.5.2009 The renormalization group : fixed points, critical exponents and universality. (Plischke and Bergerson, Huang)

End of the course