# SM0: The physics of fluctuations

Posted September 8th, 2009 by mpags
SM0
Module title: The
physics of fluctuations (SM0)

Module convenor: Prof. Juan P. Garrahan (Nottingham)

The aim of this module is to introduce elementary ideas and methods in common use in modern statistical mechanics to deal with systems subject to stochastic fluctuations. The module provides a basis for other MPAGS modules on advanced statistical mechanics (SM1 on phase transitions and collective phenomena, SM2 on statistical field theoretical methods, etc.). Teaching will consist of two one hour lectures per week. (Lectures are shared with Nottingham 4th year Math-Phys module F34AY3.) Lecture notes and other relevant files are attached at the bottom of this page.

Syllabus:

On completion of the module, students should,

Module convenor: Prof. Juan P. Garrahan (Nottingham)

The aim of this module is to introduce elementary ideas and methods in common use in modern statistical mechanics to deal with systems subject to stochastic fluctuations. The module provides a basis for other MPAGS modules on advanced statistical mechanics (SM1 on phase transitions and collective phenomena, SM2 on statistical field theoretical methods, etc.). Teaching will consist of two one hour lectures per week. (Lectures are shared with Nottingham 4th year Math-Phys module F34AY3.) Lecture notes and other relevant files are attached at the bottom of this page.

Syllabus:

- Brownian motion & Langevin theory.
- Brownian particle in a well. Fokker-Planck equation.
- Kramer's equation. Master and Boltzmann equations.
- Fluctuations in one-dimensional systems. Instabilities.
- First passage & escape problems.

On completion of the module, students should,

- be able to describe mathematically the effects of random processes, and to solve problems on this topic;
- be able to describe how fluctuations appear at instabilities and how they evolve;
- be able to describe and apply a range of theoretical approaches (mostly analytical, but also computational) currently used to describe fluctuating systems;
- be able to solve a range of problems using these techniques.

Duration:

1h on Mon, 1h on Wed (except first week)Academic year:

2009-2010Starts:

07/10/2009 - 09:15