Tracing chaos in the quantum world

Professor Pär Kurlberg will receive funding from Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Department of Mathematics, KTH Royal Institute of Technology, Stockholm.
The aim of the project is to explore issues within mathematical physics and dynamics using methods from number theory. Of special interest here is quantum chaos which involves studies of the relationship between classical chaos and quantum mechanics. 

In a classical chaotic system, small differences in initial conditions are quickly amplified, making long time predictions impossible. A striking example of this is that the possibility of our planetary system being chaotic cannot be ruled out, which could mean that the Earth will be thrown out of the solar system long before the sun turns into a red giant in about four billion years.

A fundamental feature of a classic chaotic system is the very complicated picture of closely intertwined trajectories that eventually become divergent. However, unlike the exact trajectories of classical physics, the particle trajectories in the world of quantum mechanics are not unambiguously given, they are 'smeared out', or blurred, due to Heisenberg's uncertainty principle.

Thus, a lively debated question then becomes: how can macroscopic chaos arise in a universe that is basically governed by the laws of quantum mechanics? In mathematical physics, the question is formulated into a question of how chaos in classical dynamic systems can manifest itself in the form of properties of the quantum mechanical system. Searching for the fingerprints of chaos in quantum mechanics, which is the goal of the project, often gives rise to problems that can be tackled by number theory methods. Sometimes it will also be the other way around – the questions turn out to be very interesting also from the point of view of a classical number theory.