Mathematics of anyons and intermediate quantum statistics

This proposed research project is in mathematical physics and concerns the surprising fact that, in quantum mechanics, less space implies greater variety.

There is a fundamental division of the elementary particles of ordinary three-dimensional space into two types — bosons and fermions — satisfying very different quantum statistical properties, and these have after almost a century of intense research been put to use in today´s technology in the form of new materials, microelectronics, lasers, etc.

However, quantum systems confined to lower dimensions may exhibit other types of effective emergent particles, generally called anyons, which have properties intermediate to bosons and fermions.

Despite such concepts having been around now for half a century, and investigated in many hundreds of publications by prominent physicists and even mathematicians, knowledge of the fundamental properties of such anyons is still very limited because of a lack of applicable mathematical techniques.

The purpose of this project is to develop new mathematics in the form of spectral, functional and variational methods, to settle some of the most important questions.

The project consists of five challenging objectives, with both dependent and independent tasks, some of which will be assigned to a PhD student or postdoc.

It also includes opportunities for international exchange within the PI´s network, in particular in Copenhagen, Lyon, Milan, Munich, Vienna and Zurich.