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CHM 630: Advanced Statistical Mechanics (4)

Prerequisites: CHM322/CHM642/PHY303, CHM421/PHY306 or their equivalent

Basic postulates and ensembles: Distributions, partition functions and calculation of thermodynamic properties in various ensembles.

Classical Statistical Mechanics: Classical partition function (rotational, vibrational and translational) as the high-temperature limit of its quantum counterpart, microscopic equations of motion, phase space, phase space vectors and Liouville’s theorem, the Liouville equation and equilibrium solutions, ergodic theory.

Theory of imperfect gases: Cluster expansion for a classical gas, evaluation of cluster integrals, virial explansion of the equation of state, evaluation of the virial coefficients, law of corresponding states.

Theory of the liquid state: Definition of distribution and correlation functions, radial distribution function, Kirkwood integral equation, potential of mean force and the superposition approximation, Ornstein-Zernicke equation, Percus-Yevick and hypernetted-chain approximations., density expansion of the pair functions, perturbation theory of the van der Waals’ equation.

Critical phenomena: Critical behaviour of the van der Waals equation, Ising model, lattice-gas model and binary alloys, broken symmetries, mean-field theories, Landau-Ginsburg theory, scaling and universality, introduction to renormalization group theory.

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