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MMath&Phys Mathematics and Physics / Course details
Year of entry: 2022
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Course unit details:
Advanced Statistical Physics
|Unit level||Level 4|
|Teaching period(s)||Semester 1|
|Offered by||Department of Physics & Astronomy|
|Available as a free choice unit?||No|
Advanced Statistical Physics (M)
|Unit title||Unit code||Requirement type||Description|
|Introduction to Quantum Mechanics||PHYS20101||Pre-Requisite||Compulsory|
To understand the nature and scope of the dynamical description of the macroscopic world based on statistical principles.
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.
- 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.
Feedback will be available on any students’ request.
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)
|Scheduled activity hours|
|Assessment written exam||1.5|
|Independent study hours|
|Alexander Grigorenko||Unit coordinator|