PX3A7-15 Statistical Physics
Introductory description
The collective behaviour of large numbers of interacting components in a system can lead to the emergence of novel structures and patterns. Phase transitions, the configurations taken up by polymers, and stock market trends are examples. This module looks at how we classify this behaviour, how the different classes of behaviour come about, and how we model it quantitatively.
We will start by revising statistical mechanics which is the natural starting point for describing how patterns are nucleated and grow from initial fluctuations. We will discuss how collective behaviour can be related to order parameters and how these can change across phase transitions.
Module aims
The module should illustrate the important concepts of statistical physics using simple examples. It should give an appreciation of the fundamental role played by fluctuations in nature.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Review of the fundamental principles underlying conventional statistical mechanics and thermodynamics
Phase Separation. Entropy of mixing, Interfacial tension, Cahn-Hilliard equation
Ising model. Mean field theory, solution in 1D
Landau's theory of phase transitions. Ferromagnets, Liquid crystals, dynamics
Polymers. Persistence length, elasticity, Flory theory
Brownian motion. Thermal motion, equipartition, motion of a Brownian particle; diffusion, Smoluchowski equation; correlation functions, fluctuations
Learning outcomes
By the end of the module, students should be able to:
- Work with equilibrium thermodynamics
- Describe the statistical mechanics of long chain molecules (polymers)
- Work with the Landau theory of phase transitions
- Characterise fluctuations statistically
Indicative reading list
F. Mandl, Statistical Physics, Wiley David Chandler, Introduction to Modern Statistical Mechanics, OUP P-G de Gennes Scaling Concepts in Polymer Physics, Cornell Univ. Press G Rowlands, Non-Linear Phenomena in Science and Engineering, Ellis Horwood James P. Sethna Statistical mechanics: entropy, order parameters, and complexity OUP 2007
View reading list on Talis Aspire
Subject specific skills
Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking
Transferable skills
Analytical, communication, problem-solving, self-study
Study time
| Type | Required |
|---|---|
| Lectures | 30 sessions of 1 hour (20%) |
| Private study | 120 hours (80%) |
| Total | 150 hours |
Private study description
Reading, working on problems
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Assessment group B1
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination | 100% | No | |
|
Answer 3 questions
|
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Feedback on assessment
Personal tutor, group feedback
Courses
This module is Option list A for:
- Year 3 of UMAA-G100 Undergraduate Mathematics (BSc)
- Year 3 of UMAA-G103 Undergraduate Mathematics (MMath)
- Year 4 of UMAA-G101 Undergraduate Mathematics with Intercalated Year
- Year 3 of UPXA-F300 Undergraduate Physics (BSc)
-
UPXA-F303 Undergraduate Physics (MPhys)
- Year 3 of F300 Physics
- Year 3 of F303 Physics (MPhys)
- Year 4 of UPXA-F301 Undergraduate Physics (with Intercalated Year)
- Year 3 of UPXA-F3FA Undergraduate Physics with Astrophysics (MPhys)
This module is Option list B for:
-
UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
- Year 4 of G105 Mathematics (MMath) with Intercalated Year
- Year 5 of G105 Mathematics (MMath) with Intercalated Year
-
UMAA-G103 Undergraduate Mathematics (MMath)
- Year 3 of G103 Mathematics (MMath)
- Year 4 of G103 Mathematics (MMath)
- Year 4 of UMAA-G107 Undergraduate Mathematics (MMath) with Study Abroad
- Year 4 of UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
- Year 3 of UPXA-GF13 Undergraduate Mathematics and Physics (BSc)
-
UPXA-FG31 Undergraduate Mathematics and Physics (MMathPhys)
- Year 3 of GF13 Mathematics and Physics
- Year 3 of FG31 Mathematics and Physics (MMathPhys)
- Year 4 of UPXA-GF14 Undergraduate Mathematics and Physics (with Intercalated Year)