# Order in chaos

Simplifying quantum theory

There are exceptional trajectories, which always stay in a small part of the space

Ever since the birth of quantum theory early last century, mathematicians and scientists have been attempting to simplify it. Their aim is to pinpoint situations in which the complex, counter-intuitive system of mathematics describing the subatomic realm can be approximated by the classical physics developed in the seventeenth century.

Dr Andrew Hassell of MSI has built a bridge between aspects of quantum mechanics and classical physics in work centred on a field called quantum chaos. He considered the chaotic motion of an object, such as a billiard ball, bouncing off the walls of a two-dimensional space the shape of a soccer stadium.

“In the classical setting, almost every billiard ball trajectory spends the same amount of time in every region of the space in the long term,” says Hassell. “But there are exceptional trajectories, which always stay in a small part of the space. There’s been a long-standing question in quantum chaos asking whether there are exceptional quantum trajectories corresponding to these exceptional classical trajectories. In this ‘stadium’ example, I showed that there were indeed such exceptional quantum trajectories.”

The result, which caused a stir in the international mathematical community, could find applications in theoretical chemistry – in the prediction of the properties of large atoms through computer models drawing on quantum theory. Hassell’s billiard ball would act as an analog of an electron.

Although his work is theoretical mathematics, it may find application in the design of nanoelectronic devices, such as quantum dots, which might eventually form the building blocks of quantum computers.