Vortex dynamics is an excellent example of emerging behavior. It plays important role in both basic and applied research with wide range of applications. For example, it is responsible for the flight of airplanes and is a key factor for the applications of superfluids and superconductors. I will discuss vortex dynamics from Landau’s fiat on its absence in his Nobel prize winning work on theory of superfluid helium in the current setting. During past two decades there are huge activities on vortex matter in both superfluids and superconductors. However, the discussion of its fundamental equation of motion from microscopic theories has been sparse. I will thus talk about our effort to clarify various theoretical issues on vortex dynamics and why they are so difficult. I will also discuss a few experimental efforts to test the fundamental equation and implications in more general terms.
Suggested references: 1. Berry's Phase and the Magnus Force for a Vortex Line in a Superconductor，Ao & Thouless, PRL 70, 2158 (1993); 2. Microscopic Theory of Vortex Dynamics in Homogeneous Superconductors， Ao & Zhu, PR B60, 6850 (1999)；3. Lessons from vortex dynamics in super media，Ao, cond-mat/0407007