Statistical Mechanics - Core (PHY 215.5)

Venue: Online

Class timings: Wednesdays and Fridays 4:00 PM to 05:30 PM

First meeting: 15th September, 2021

Course description: 

    • Recap of Fundamentals of thermodynamics, Probability, distributions 

    • 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 —— Revisit phonons, photons —— Landau diamagnetism 

    • Introduction to simulation methods

    • Interacting classical gas —— Virial expansions —— Cumulant expansions —— Liquid state physics —— Van-der Waals equation

    • Introduction to Phase transitions and Critical phenomena, universality, mean field theory, some exactly solvable models. 

Textbooks:

    • M. Kardar, Statistical Physics of Particles

    • R. K. Pathria, Statistical mechanics

    • K. Huang, Statistical mechanics

    • J. M. Sethna, Statistical Mechanics: Entrop, Order Parameters and Complexity

    • M. Kardar, Statistical Physics of fields

    • Landau & Lifshitz, Statistical mechanics

    • + some other books and papers, references of which will be provided in the class.

Course evaluation: 

50% Assignment + 25% mid sem exam + 25% end sem exam