AMA4004: Statistical Mechanics
Description
Statistical mechanics is a formalism that aims to explain the physical properties of matter at the macroscopic level by considering the dynamical behaviour of matter's microscopic constituents - atoms and molecules. The scope of the formalism is almost unlimited as it is applicable to matter in any state of aggregation, ranging from gases, liquids and solids to matter in equilibrium with radiation and biological specimens. The aim of this course is to introduce the basic principles and methods of statistical mechanics and to apply them to a number of model systems in order to illustrate their use and potential in a systematic manner. We start by introducing the fundamentals of thermodynamics and then proceed to develop the concepts and techniques needed to evaluate probability distributions and partition functions. This later quantity establishes the link between the microscopic description of a system, based on quantum states or positions in phase space, and the macroscopic characterisation provided by a small set of independent thermodynamic variables. We discuss a number systems where the partition function can be calculated exactly and then show how we can use this function to rationalise the behavior of the constituent particles in these system at the microscopic and macroscopic scales. Ultimately, however, the exact solution for the partition function cannot be found for the majority of real systems of interest. In the last part of the course we therefore discuss how approximate ensemble averages are found by exploiting approximations or numerical simulation techniques.
Assessment
The module assessment consists of the following activities:
| item | due date | weight |
| A 40 minute class test on classical thermodynamics | Friday of week 3 | 10 |
| One portfolio of work done during the semester | Tuesday of week 12 | 20 |
| One presentation and report on a scientific paper. | Fridays of weeks 10 and 12 | 20 |
| One three hour examination in which all questions on the paper must be answered | April exam period | 50 |
Details on what you are expected to work on during each week of the semester can be found by clicking here .
A summary of some of the key ideas and theorems that are introduced in this module can be found by clicking here .
Portfolio projects
The final aspect of the assessment for this module is a portfolio for which you must produce projects on the following:
- Classical thermodynamics
- Statistical mechanics applications
- Statistical mechanics theory
- Computer simulations
Details on how your final portfolio will be assessed can be found by clicking here .
Some questions to think about when writing your weekly reports can be found by clicking here .