1. Statistical Mechanics and Soft Condensed Matter
Brownian motion
by Pietro Cicuta

2. Slide 1: The movement of particles in a fluid can be described in terms of the average behaviour of a large number of particles in random motion. Reprinted with permission from MIT (Figure is credited to Ziad Ganim).

3. Fick’s first law of diffusion:
Fick’s second law:
if D is independent of concentration
Slide 2: Diffusion.

4. For a walk in one dimension:
In 3 dimensions:
In d dimensions:
Slide 3: Random walk. (Ziad Ganim, reprinted with permission from MIT.)

5. Slide 4: General equation of motion for a particle in a fluid.

6. an example of the fluctuation dissipation theorem
Slide 5: Solutions when the force is “random noise”.

7. Einstein relation:
Stokes–Einstein relation:
Slide 6: Mean square displacement.