Venue: Emmy Noether Seminar Room
Class Timings: Tuesdays & Thursdays from 2:00 PM - 3:30 PM
First Meeting: 13 August 2024
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
Course Outcome:
- 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
- Teacher: Samriddhi Sankar Ray