PHYS-507 Statistical Mechanics
Fall for 2017-2018
The objective of this course is to introduce the student to today’s understanding of statistical physics and statistical mechanics. The course begins with a review of thermodynamics. Next comes a brief introduction to probability and statistics. This is followed by the heart of the course, equilibrium statistical mechanics. The microcanonical, canonical, and grand canonical ensembles will be considered and some other ensembles will be noted. Both classical and quantum systems will be investigated. Most applications will focus on systems of non-interacting particles, although some of the techniques for dealing with classical interacting systems will be noted and one or two selected interacting quantum systems will be briefly considered. The first applications will be to a system of localized spins, vacancies in a solid, and a rubber band. Then, Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics will be discussed and applied to the classical gas, electrons in a metal, blackbody radiation (photons), lattice vibrations (phonons), the ideal Bose-Einstein gas, and the Ising model. If time allows, second quantization will be introduced and applied to one or two of these systems. The last portion of the course will be principally concerned with phase transitions, specifically first order phase transitions, phase separation, continuous phase transitions, and the Landau theory of phase transitions. As time allows and where appropriate, the Ginzburg-Landau theory of inhomogeneous phase transitions and some of the ideas and applications of non-equilibrium statistical physics will be entertained.
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