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. 

• 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