Statistical Mechanics - Core (PHY 205.5)

Venue:  Chern Lecture Hall on Mondays and Emmy Noether Seminar Hall on Wednesdays

Class Timings: Mondays from 11:30 AM - 1:00 PM and Wednesdays from 1:45 PM - 3:15 PM

First Meeting: 11 August 2025 

Course Syllabus: 

• Recap of Fundamentals of thermodynamics, Probability, distributions
• Kinetic theory of gases: BBGKY hierarchy,  Boltzmann equation, H-Theorem and Irreversibility
• Foundations of equilibrium statistical mechanics —- Liouville’s equation, microstate, macrostate, phase space, typicality ideas, (Little on irreversible evolution of macrostate), Kac ring, equal a priori probability, ensembles as tools in statistical mechanics.
• Partition functions, connection to thermodynamical free energies, Response functions
• Examples: Non-interacting systems —— Classical ideal gas, Harmonic oscillator, paramagnetism, adsorption, 2 level systems, molecules, more non-standard examples.
• Formulation of quantum statistical mechanics —— Quantum microstates, Quantum macro-states, density matrix.
• Quantum statistical mechanical systems —— Dilute polyatomic gases, Vibrations of solid, Black body radiation
• Quantum ideal gases —— Hilbert space of identical particles —— Fermi gas, Pauli paramagnetism —— Bose gas, BEC —— phonons,  photons —— Landau diamagnetism 
• Interacting classical gas ——— Mean field theory, Ising Model, virial expansions and Van-der Waals Gas

• Have an understanding of the basic principles of equilibrium statistical mechanics including kinetic theory and the Boltzmann-Gibbs ensemble theory
• Understand applications to few body and non-interacting many body  systems such as ideal gases, harmonic crystals, photons
• Understand some examples of interacting systems and approximate methods such as mean field theory and perturbation theory
• Develop analytical and numerical problem solving skills