Final assessment by means of written and/or oral exams.
Learning
objectives
The course aims to provide the skills needed to use statistical mechanics and its applications in the various areas of physics. In particular, it develops an understanding of the various canonical ensembles and their physical applications to gases, condensed matter and field theory.
Contents
Elements of thermodynamics: First law and equilibrium. Second law. Variational formulation of the second law. Thermal equilibrium and temperature. Auxiliary functions and Legendre transforms. Maxwell relations. Extensive functions and the Gibbs-Duhem equation. Intensive functions. Principles of statistical mechanics: The fundamental postulate. Statistical method and ensembles. Microcanonical ensemble. Canonical ensemble. Examples. Generalised ensembles and Gibbs formula for entropy. Variational derivation of equilibrium distributions. Phase transitions: Ising model. Lattice gas. Symmetry breaking and coherence length. Ising model. Mean-field theory. Critical exponents. Scaling. Outline of the real-space renormalisation group: Migdal-Kadanoff renormalisation group. Foundations of Quantum Statistical Mechanics: Density matrix.
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