The overall goal is to obtain a rigorous understanding of specific problems originating from physics.
Originally, the mathematics used in physics consisted mainly of differential geometry and partial differential equations, with intuition playing a strong role. As a culmination, the theories of relativity were formulated entirely in this framework. In addition statistical mechanics was based on probability theory. In quantum mechanics, however, it has been necessary to adopt also Hilbert space methods and operator theory.
Today, many other advanced techniques from mathematical analysis (and beyond) have proved useful in the treatment of mathematical physics."
Topics of recent and current interest include:
- Light interacting with matter.
- Magnetic perturbation theory.
- Non-homogeneous parabolic boundary value problems in mixed-norm spaces.
- Partial differential equations and control theory.
- Quantum scattering theory for many-body systems.
- Quantum transport in mesoscopic systems.
- Quasi-particles in carbon nanotubes.
- Quantum Monte Carlo methods in nanophysics.
- Semi-linear elliptic boundary value problems.
Members of this group and their research interests
- Horia Cornean and Mikkel Haggren Brynildsen works on quantum transport, spectral analysis of magnetic Schrödinger and Harper operators.
- Arne Jensen works on spectral and scattering theory for Schrödinger operators, theory of resonances for Schrödinger operators, Schrödinger operators with explicitly time-dependent interactions, threshold asymptotics for resolvents of Schrödinger operators.
- Jon Johnsen works on works on semi-linear problems and Non-homogeneous parabolic boundary value problems in mixed-norm spaces.
- Ann-Eva Christensen works on Partial differential equations and control theory.
- Sabrina Munch Hansen works on non-homogeneous parabolic boundary value problems in mixed-norm spaces.
Information on relevant publications can be found via the VBN Database.