- UCAS course code
- F3FA
- UCAS institution code
- M20
Course unit details:
Advanced Statistical Physics
Unit code | PHYS40571 |
---|---|
Credit rating | 10 |
Unit level | Level 4 |
Teaching period(s) | Semester 1 |
Available as a free choice unit? | No |
Overview
Advanced Statistical Physics (M)
Pre/co-requisites
Unit title | Unit code | Requirement type | Description |
---|---|---|---|
Introduction to Quantum Mechanics | PHYS20101 | Pre-Requisite | Compulsory |
Statistical Mechanics | PHYS20352 | Pre-Requisite | Compulsory |
Aims
To understand the nature and scope of the dynamical description of the macroscopic world based on statistical principles.
Learning outcomes
On completion successful students will:
- Be able to explain what a Markov process is and to use analytical methods to study the dynamics of Markovian systems.
- Understand the origin of the irreversibility seen at the macroscale including examples which illustrate the essential ideas behind the fluctuation-dissipation theorem; be familiar with modern concepts relating equilibrium and non-equilibrium statistical physics. Bbe able to show how different kinds of description of stochastic processes are related, especially the idea of a microscopic model and its relation to a macroscopic model.
- Be able to perform straightforward calculations for systems which are described by stochastic dynamics, determining stationary probability distributions from master or Fokker-Planck equations and correlation functions from Langevin equations.
- Be familiar with the basic numerical methods used to simulate stochastic dynamical systems.
Syllabus
- Stochastic variables and stochastic processes
Revision of the basic ideas of probability theory; probability distribution functions; moments and cumulants; characteristic functions; the central limit theorem and the law of large numbers.
- Markov processes
The Chapman-Kolmogorov equation; Markov chains; Applications: (random walk, birth-death process); the master equation; methods of solution of the master equation; efficient simulation methods for Markov processes with discrete states.
- Drift and diffusion
The Fokker-Planck equation: derivation and methods of solution; relation to Schrödinger’s equation; applications to barrier crossing, activation and mean-first-passage times.
- Stochastic differential equations
The Langevin equation and its generalisations; analytical and numerical methods of solution; applications to Brownian motion.
- Modern topics in statistical physics
Fluctuation theorems; statistical physics of small systems; applications to complex systems modelling.
Assessment methods
Method | Weight |
---|---|
Written exam | 100% |
Feedback methods
Feedback will be available on any students’ request.
Recommended reading
Gardiner, C. Stochastic Methods, A Handbook for the Natural and Social Sciences (Springer)
Jacobs, K. Stochastic Processes for Physicists, Understanding Noisy Systems (Cambridge University Press)
Reichl, L.E. A Modern Course in Statistical Physics, 2nd ed, (Wiley)
Study hours
Scheduled activity hours | |
---|---|
Assessment written exam | 1.5 |
Lectures | 24 |
Independent study hours | |
---|---|
Independent study | 74.5 |
Teaching staff
Staff member | Role |
---|---|
Jeffrey Forshaw | Unit coordinator |