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Semester 2
Statistical Mechanics (PHYS09019)
Subject
Physics and Astronomy
College
SCE
Credits
10
Normal Year Taken
3
Delivery Session Year
2023/2024
Pre-requisites
Course Summary
This course provides an introduction to the microscopic formulation of thermal physics, generally known as statistical mechanics. We explore the general principles, from which emerge an understanding of the microscopic significance of entropy and temperature. We develop the machinery needed to form a practical tool linking microscopic models of many-particle systems with measurable quantities. We consider a range of applications to simple models of crystalline solids, classical gases, quantum gases and blackbody radiation.
Course Description
- Statistical description of many-body systems; formulation as a probability distribution over microstates; central limit theorem and macrostates.- Statistical mechanical formulation of entropy. - Minimisation of the free energy to find equilibrium.- Derivation of the Boltzmann distribution from principle of equal a priori probabilities in extended system. - Determination of free energy and macroscopic quantities from partition function; applications to simple systems (paramagnet, ideal gas, etc). - Multi-particle systems: distinguishable and indistinguishable particles in a classical treatment; Entropy of mixing and the Gibbs paradox.- Fermi-Dirac distribution; application to thermal properties of electrons in metals.- Bose-Einstein distribution; application to the properties of black body radiation; Bose-Einstein condensation.- Introduction to phase transitions and spontaneous ordering from a statistical mechanical viewpoint: illustration of complexity arising from interactions; simple-minded mean-field treatment of an interacting system (e.g., van der Waals gas, Ising model); general formalism in terms of Landau free energy. - Introduction to stochastic dynamics: need for a stochastic formulation of dynamics; principle of detailed balance; relaxation to equilibrium; application to Monte Carlo simulation; Langevin equation and random walks.
Assessment Information
Written Exam 80%, Coursework 20%, Practical Exam 0%
Additional Assessment Information
Coursework, 20%Degree Examination, 80%
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