# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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DRPS : Course Catalogue : School of Physics and Astronomy : Undergraduate (School of Physics and Astronomy)

# Undergraduate Course: Statistical Mechanics (PHYS09019)

 School School of Physics and Astronomy College College of Science and Engineering Credit level (Normal year taken) SCQF Level 9 (Year 3 Undergraduate) Availability Available to all students SCQF Credits 10 ECTS Credits 5 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.
 Pre-requisites Students MUST have passed: Classical and Modern Physics (PHYS08044) OR Modern Physics (PHYS08045) Students MUST have passed: Dynamics (PHYS08040) OR Dynamics and Vector Calculus (PHYS08043) Co-requisites Prohibited Combinations Students MUST NOT also be taking Thermal Physics (PHYS09061) OR Thermodynamics (PHYS09021) Other requirements None
 Pre-requisites None High Demand Course? Yes
 Academic year 2019/20, Available to all students (SV1) Quota:  None Course Start Semester 2 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 22, Summative Assessment Hours 8, Revision Session Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 44 ) Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 % Additional Information (Assessment) Coursework, 20% Degree Examination, 80% Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S2 (April/May) 2:00
 On completion of this course a student should be able to: 1)define and discuss the concepts of microstate and macrostate of a model system 2)define and discuss the concepts and roles of entropy and free energy from the view point of statistical mechanics 3)define and discuss the Boltdsmann distribution and the role of the partition function 4)apply the machinery of statistical mechanics to the calculation of macroscopic properties resulting from microscopic models of magnetic and crystalline systems 5)discuss the concept and role of indistinguishability in the theory of gases; know the results expected from classical considerations and when these should be recovered 6)define the Fermi-Dirac and Bose-Einstein distributions; state where they are applicable; understand how they differ and show when they reduce to the Boltsman distribution 7)apply the Fermi-Dirac distribution to the calculation of thermal properties of elctrons in metals 8)apply the Bose-Einstein distribution to the calculation of properties of black body radiation
 None
 Graduate Attributes and Skills Not entered Additional Class Delivery Information Workshop/tutorial sessions, as arranged. Keywords StatM
 Course organiser Dr Alexander Morozov Tel: (0131 6)50 5289 Email: alexander.morozov@ed.ac.uk Course secretary Miss Denise Fernandes Do Couto Tel: (0131 6)51 7521 Email: Denise.Couto@ed.ac.uk
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