Statistical Mechanics II - Topical (PHY 215.5/ BIO 215.5)

Venue: Emmy Noether Seminar Room

Class Timings:  Mondays & Wednesdays from 02:00 PM - 03:30 PM

First Meeting: 08 January 2025

Course Outline: 

Part (1): Equilibrium (16-18 Lectures)

• Equilibrium  and equilibrium ensembles,  the thermodynamic limit
• Interacting systems in 1d,  transfer matrix formulation
• 2d Ising model, quantum spin chains
• Series expansions: cluster expansions, weak and strong coupling expansions
• Correlation functions and liquid state theory
• Phase transitions: phenomenology and mean-field  and Landau- Ginzburg theory
• Renormalization Group theory

Part(2): Non-equilibrium (10-12 lectures)

• Brief review of Kinetic theory of gases: BBGKY hierarchy,
• The Boltzmann equation, H-Theorem and Irreversibility
• Transport theory
• Stochastic Processes:  Random walk, Brownian motion, Markov Processes Master equation, Fokker-Planck equation Linear response theory

References:

• Statistical Physics, Reif
• Statistical Physics of particles, M. Kardar
• Statistical Physics of fields, M. Kardar
• Statistical Mechanics, R. K. Pathria and P. D. Baule
• Statistical Physics, L.D. Landau and E. M. Lifshitz
• Statistical Mechanics,  S K Ma
• Statistical Mechanics , James P Sethna
• Statistical Mechanics: D  Chowdhury and D Stauffer
• Probability theory and applications: W Feller
• An Introduction to exactly solved models in Statistical physics, G Mussardo

Course Outcome:

• Learn the macroscopic and microscopic description of a system with many degrees of freedom. 
• Appreciate the importance of disparity in the volume of phase spaces associated with different macro-states due to a large number of degrees of freedom. 
• Learn the formulation of statistical mechanics and connection to thermodynamics, and also the basic ensemble descriptions.
• Learn to use the tools provided by the ensemble descriptions and calculate thermodynamic quantities. 
• Understand the statistical properties of non-interacting systems, e.g. phonons, photons, ideal gas, etc. 
• Understand the importance of the difference of statistics of fermions and bosons and its implications on the emergent thermodynamics properties.