Class timings: Wednesdays and Fridays 4:00 PM to 05:30 PM
First meeting: 15th September, 2021
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.
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.
50% Assignment + 25% mid sem exam + 25% end sem exam