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Statistical Physics (MATH327), Spring 2021

Probabilistic processes provide often-outstanding mathematical descriptions of systems within the domain of statistical physics. This course introduces the foundations of statistical physics, including the concepts of statistical ensembles, the laws of thermodynamics, and derived quantities such as entropy. These foundations will be applied to investigate diffusion, the behaviour of idealized physical systems such as classical and quantum gases, thermodynamical cycles, and phase transitions. In particular, computer simulations will be used to numerically investigate diffusion and transport in terms of stochastic processes.

Learning outcome

Upon completing this module, students are able to:

Resources

This module is intended for third- and fourth-year undergraduates as well as students in the one-year taught MSc programme. Familiarity with combinatorics and quantum mechanics is not assumed. Any necessary information from those disciplines will be provided. All resources for the module will be gathered at its Canvas site.

These gapped lecture notes are the main learning resource. They are kept under version control at GitHub, providing an easy way to monitor any typo fixes or other improvements. Reports of any issues, and pull requests to address them, are also welcome.

My office hours are still to be set. You can also make an appointment to meet with me at other times.

As you know by this point in your studies, the best way to learn mathematics is by doing mathematics. This includes (but is not limited to!) making sure you can fill in the gaps in the lecture notes, complete the tutorial exercise and solve the homework problems (yourself, though I encourage you to discuss these problems with each other). Sample exams are also available to allow additional practice. When you ask me questions about these exercises and problems, I will endeavour to avoid doing this work for you; instead I will have you explain to me what you have tried so far, and will ask leading questions to suggest where I see problems or potential next steps.

In addition to the gapped lecture notes, potentially useful statistical physics references at roughly the level of this module include:

There are also many textbooks at a higher level than this module, including the following:

Schedule

Week 1 (8–14 February): Central limit theorem and diffusion

Week 2 (15–21 February): Micro-canonical ensemble

Week 3 (22–28 February): Canonical ensemble

Week 4 (1–7 March): Ideal gases

Week 5 (8–14 March): Thermodynamic cycles

Week 6 (15–21 March): Grand-canonical ensemble

Week 7 (12–18 April): Quantum statistics

Week 8 (19–25 April): Quantum gases of bosons

Week 9 (26 April – 2 May): Quantum gases of fermions

Week 10 (3–9 May): Interacting systems

Week 11 (10–16 May): Synthesis and broader applications



Last modified 7 January 2021

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