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
|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.
- 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.
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2022/23, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
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
|Assessment (Further Info)
|Additional Information (Assessment)
Degree Examination, 80%
||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
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
|Graduate Attributes and Skills
|Additional Class Delivery Information
||Workshop/tutorial sessions, as arranged.
|Course organiser||Dr Alexander Morozov
Tel: (0131 6)50 5289
|Course secretary||Miss Emma Summers
Tel: (0131 6)51 7524