Newton's laws of motion accurately describe how relatively large objects move, but they fail for very small objects. They then have to be replaced by quantum mechanical laws of motion. For example, quantum mechanics is needed to describe the dynamics of the electrons inside atoms and molecules.
The borderland where Newton's laws give way to quantum mechanics is mathematically extremely interesting, particularly when the Newtonian dynamics is chaotic. It is also of considerable experimental and technological importance, because the size of many microelectronic and optical devices currently being developed, such as microprocessors and microlasers, puts them in this crossover range.
Some of the most fundamental developments in the field of quantum chaos – the study of how the chaotic nature of Newtonian dynamics influences quantum mechanical behaviour in the crossover range – are associated with research carried out in Bristol. These include pioneering the statistical description of the values taken by quantum wave functions, the use of Newtonian dynamics to approximate quantum energy levels and to predict their statistical distribution, and the theory of discrete quantum chaotic dynamical systems.
The field of quantum chaos is developing rapidly. It brings together recent ideas from analysis, dynamical systems, number theory, probability theory and quantum physics, and covers an extremely broad spectrum of activity, from experimental physics to pure mathematics.