Basic introduction to phase transitions: first order and continuous; Critical phenomena: critical exponents and scaling hypothesis; Ising model: exact solution in one dimension, mean-field approximation and calculation of critical exponents, Landau theory; Review of probability theory: Law of large numbers and the central limit theorem; Random walk; Brownian motion: Langevin and Fokker-Planck descriptions; Fluctuation-Dissipation theorem; Markovian process; Master equation; Concept of steady states, detailed balance and equilibrium vs. non-equilibrium.

Review of thermodynamics; Objectives of statistical mechanics; Microstates and macrostates; Phase space and concept of an ensemble; Liouville’s theorem and concept of equilibrium; Ergodic hypothesis and postulate of equal a priori probability; Microcanonical ensemble: Boltzmann’s definition of entropy and derivation of thermodynamics; The equipartition theorem; Microcanonical ensemble calculations for a classical ideal gas; Gibbs paradox; Canonical ensemble; Energy fluctuations in the canonical ensemble; Grand canonical ensemble; Density fluctuations in the grand canonical ensemble; Quantum statistical mechanics: Postulate of equal a priori probability and postulate of random phases; Density matrix; Ensembles in quantum statistical mechanics; The ideal quantum gas: Microcanonical and grand canonical ensembles; Fermi-Dirac and Bose-Einstein statistics; Bose-Einstein condensation.

Action principle formulation of a relativistic particle; Electromagnetic (EM) fields: relativistic formulation; Action formulation of EM fields: Maxwell equations; The vector potential: relativistic formulation; Interaction of EM fields with currents: Noether’s theorem; Interaction of charged particle with EM fields: Lorentz force equations, examples; Energy Momentum tensor: Conservation and Poynting’s theorem; Vacuum EM waves: geometrical optics limit; polarisation, Stokes parameters and Poincare sphere; EM waves in media: Faraday rotation; EM potentials due to an arbitrarily moving charged particle; EM fields from the moving charges: radiation and Coulomb fields; Dipole radiator: Larmor’s formula, radiated power spectrum; Synchrotron radiation: radiated power spectrum; polarization; Classical scattering of EM waves by charges: Rayleigh and Thomson scattering; Elements of multipole radiation: E1, E2 and M1 modes; Radiation reaction and inconsistencies of the Maxwell theory