MATH4231: Statistical Mechanics IV

• Analysis in Many Variables (MATH2031) AND [Mathematical Physics (MATH2071) OR Theoretical Physics 2 (PHYS2631)] AND additional Mathematical Sciences modules to the value of 60 credits in Levels 2 and 3, with at least 40 credits at Level 3.

• None

• Foundations of Physics 3B (PHYS3631)
• Foundations of Physics 4B (PHYS4261)

• To develop a basic understanding of the dynamics and behaviour of systems with a large number of constituents.
• To develop approximation techniques and calculational methods to understand collective dynamics of large particle ensembles.

• Thermal equilibrium, laws of thermodynamics, equations of
• state, ideal gas law.
• Probability distributions and random walks.
• Classical statistical mechanics.
• Distributions and identical particles.
• Black-body radiation, magnetisation, neutron stars.
• Phase transitions.
• Reading material on one or more aspects of the
• Renormalization Group.

Subject-specific Knowledge:

• The students will:
• learn to deal with systems where statistical ideas give a good picture of the essential dynamics;
• learn to develop approximation methods necessary to solve problems involving large systems;
• master knowledge of the subject through one or more of the following subject areas: thermodynamics, probability distributions, statistical ensembles, phase transitions;
• have a knowledge and understanding of a topic in the renormalization group approach.

Subject-specific Skills:

• The students will have specialised knowledge and mathematical skills in tackling problems in: statistical modeling of large systems.
• Ability to read independently to acquire knowledge and understanding of aspects of the Renormalization Group approach.
• The students will have an appreciation of Statistical Mechanics and its utility in the real world in the study of various complex systems and solutions thereof.

Key Skills:

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

If you have a question about Durham's modular degree programmes, please visit our FAQ webpages, Help page or our glossary of terms. If you have a question about modular programmes that is not covered by the FAQ, or a query about the on-line Undergraduate Module Handbook, please contact us.

Prospective Students: If you have a query about a specific module or degree programme, please Ask Us.

Current Students: Please contact your department.