Research Fellows Directory
Professor Jens Marklof
University of Bristol
The characterization of chaos and randomness in microscopic dynamics is one of the central objectives in my research. I am particularly excited about our recent progress in the investigation of an electron gas travelling through a crystal, where the atoms of the crystal are arranged at the vertices of a cubic lattice. In a joint paper with A. Strömbergsson at Uppsala University, we explain that the randomness created by the collisions at the crystal lattice determines the evolution of a macroscopic electron cloud. This solves a puzzle posed by Dutch physicist Hendrik Lorentz (1853-1928) more than a century ago.
The breakthrough in this long-standing problem was made possible by “measure rigidity”, a relatively new branch of pure mathematics that has led to a number of important applications in several areas of pure and applied mathematics. In simplistic terms, measure rigidity may be viewed as a technical tool that can detect and characterize random phenomena without the need of heavy analysis. It is an extremely effective technique, and I am convinced we will see more spectacular applications in the future. The current focus of my research is to remove some of the simplifying assumptions in Lorentz’ model of the electron gas. In particular the incorporation of quantum theory is a crucial challenge, and it will be interesting to see whether our measure rigidity techniques can be adapted to this setting.
My research programme contributes to the understanding of the laws of nature, the emergence of chaos and randomness and their effect on large-scale particle dynamics. It uses tools from many diverse areas in mathematics and physics, and fosters the interaction between the subjects. As fundamental research, it provides the theoretical foundation for technological applications. I am hopeful that our new evolution equations will become experimentally accessible, and perhaps even contribute to innovative applications, e.g., in the design of micro-electronic devices.