Week 1: Introduction, Why study Statistical Physics, Review of Thermodynamics, Entropy, Gibb’s paradox, concept of Temperature, Free energies and their interrelationships, Legendre transformation, Maxwell’s relations, Micro and Macrostates, Examples.
Week 2: Ensembles, Different Ensembles: Microcanonical, Canonical and Grand Canonical Ensembles, concept of Phase Space, Phase Space density, Liouville’s Theorem, Lagrange’s undetermined multipliers, Partition Function.
Week 3: Application of ensemble theory to classical ideal gas, non-interacting spins in a magnetic field, Magnetization, Curie’s law, Classical Harmonic Oscillators, Specific Heat, concept of Negative Temperature, Realization of negative temperature in lab, Cold atomic systems.
Week 4: Quantum Statistics: Distribution functions for indistinguishable particles, occupation numbers, Quantum Ideal Gases, Ideal Bose and Fermi systems, resolution of Gibb’s paradox.
Week 5: Ideal Bose Gas, Bose-Einstein Condensation (BEC), properties of an ideal Bose gas, Black Body Radiation, Specific heat of solids, Einstein’s and Debye’s theories.
Week 6: Ultracold atomic systems, Recent experiments on achieving negative temperature in labs, liquid Helium, Superfluidity
Week 7: Non-interacting Fermions, Pauli Exclusion Principle, Slater determinants, Free Fermi Gas, Fermi surface and Fermi temperature of Metals, Shubnikov de Haas and de Haas van Alphen (dHvA) oscillations
Week 8: Electronic Specific heat, Magnetic Properties of Solids, Pauli paramagnetism, Semiconductors, Law of mass action.
Week 9: Special topics: White dwarfs, Chandrasekhar limit, classical and quantum black hole thermodynamics, Temperature and surface gravity.
Week 10: Interacting Systems, Formalism, Virial equation of state, Virial coefficients, different kinds of interparticle interactions, introduction to linked cluster expansions.
Week 11: Ising model in one dimension, Exact solutions, Transfer matrix, Mean field theory, Bragg-William’s approximation
Week 12: Renormalization Group, Phase transitions, fixed points, Two-dimensional Ising Model, Bethe Anstaz.
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