13 - Collective effects – grexons

Summary

‘All together now!’

Rowboat crew cox

A collapsing stock market, astronomers jumping aboard the bandwagon of the latest ‘hot topic’, rowboat crews, and galaxy formation – all are examples of collective effects. If the strokes of all the rowers in a boat have randomly distributed phases, some pulling upstream while others pull downstream, the boat at best performs a linear random walk. But if all the rowers row in phase, their strengths add nearly linearly (there is some turbulence) and away glides the boat. If buyers and sellers of stocks are about evenly balanced, the price of an average share records little change. A mild selling imbalance somewhat decreases prices. If the decrease deepens and spreads, people begin to worry that they may lose their fortunes. ‘Sell out fast!,’ the word goes 'round. Panic strikes. Everyone sells. The market collapses. In this case, not only do all the phases act together, but the action reinforces itself. It is highly non-linear and the result is catastrophe. Astrophysical bandwagons illustrate still other aspects of collective phenomena (left as an exercise for the reader).

Gravitating systems are prone to a variety of collective effects. Previously, whenever we examined the motion of a star in a system, we have always asked what the system can do to the star, not what the star can do to the system. Obviously a heavyweight star will do more to a system than a lightweight one will, and this change in the system in turn will react back on the motion of the star.