Course info

Course description:

• Recap of Fundamentals of thermodynamics, Probability, distributions (single and multi variables), Conditional probability, moments, cumulants, moment generating functions, central limit theorems
• 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 -- Integer partitions -- Condensation phenomena in real space
• Basic discussions on large deviation principles in classical statistical mechanics.
• Introduction to simulation methods
• Interacting classical gas -- Virial expansions -- Cumulant expansions -- Liquid state physics -- Van-der Waals equation

Textbooks:

• M. Kardar, Statistical Physics of Particles
• R. K. Pathria, Statistical mechanics
• K. Huang, Statistical mechanics
• J. M. Sethna, Statistical Mechanics: Entropy, 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.