**Venue:**Online

**Class timings:**Tuesday and Friday from 4:00 to 5:30 PM

**First meeting:**4th September 2020

**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.

**Evaluation:**

Assignment: 50%

Class test: 10%

End semester exam: 40%

- Teacher: Anupam Kundu