Syllabus
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Course Code: PHY 302 Course Name: Statistical Mechanics |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Classical Statistical Mechanics (14 hrs.) Foundations of Statistical Mechanics: The macroscopic and microscopic states, Postulate of equal a priori probability, Contact between statistics and thermodynamics; Entropy of mixing and the Gibbs paradox, Sackur-Tetrode equation, Ensemble theory: Concept of ensemble, Phase space, Density function, Ensemble average, Liouville‟s theorem, Stationary ensemble; The microcanonical ensemble, The canonical and grand canonical ensembles, Application to the classical ideal gas; Canonical and grand canonical partition functions, Calculation of statistical quantities; Thermodynamics of a system of non-interacting classical harmonic oscillators using canonical ensemble and of classical ideal gas using grand canonical ensemble, Energy and density fluctuations. |
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| 2 | Quantum Statistical Mechanics (14 hrs.) Quantum-mechanical ensemble theory: Density matrix, Equation of motion for density matrix, Quantum mechanical ensemble average; Statistics of indistinguishable particles, Fermi-Dirac and Bose-Einstein statistics, Fermi-Dirac and Bose-Einstein distribution functions using microcanonical and grand canonical ensembles (ideal gas only), Statistics of occupation numbers; Ideal Bose gas: Internal energy, Equation of state, Bose-Einstein Condensation and its critical conditions; Bose-Einstein condensation in ultra-cold atomic gases: its detection and thermodynamic properties; Ideal Fermi gas: Internal energy, Equation of state, Completely degenerate Fermi gas. |
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| 3 | Non-Ideal Systems (12 hrs.) Cluster expansion method for a classical gas, Simple cluster integrals, Mayer-Ursell relations, Virial expansion of the equation of state, Van der Waal’s equation, Validity of cluster expansion method; Phase transitions: Construction of Ising model, qualitative description of ferromagnetism, Lattice gas and Binary alloy, Solution of Ising model in the Bragg-William approximation, Exact solution of the one-dimensional Ising model; Critical exponents, Landau theory of phase transition, Scaling hypothesis. The role of correlation and fluctuation |
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| 4 | Fluctuations (12 hrs.) Thermodynamic fluctuations and their probability distribution law, Spatial correlations in a fluid, Connection between density fluctuations and spatial correlations; Brownian motion, Enistein-Smoluchowski theory of Brownian Motion, Langevin theory of the Brownian motion (derivations of mean square displacement and mean square velocity of Brownian particle), Auto-correlation function and its properties, The fluctuation-dissipation theorem, Diffusion coefficient; the Fokker-Planck equation; Spectral analysis of fluctuations: the Wiener-Khintchine theorem. |
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