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 Field Theory
- Semi-linear elliptic boundary value problems.
Members of this group and their research interests
- Horia Cornean works on quantum transport, spectral analysis of magnetic Schrödinger and Harper operators. Benjamin is Horia's PhD students and work in related areas.
- 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 semi-linear problems and Non-homogeneous parabolic boundary value problems in mixed-norm spaces.
- Morten Grud Rasmussen works on scattering and spectral aspects of Quantum Field Theory. Kasper is Morten's PhD student and works in related areas.
- Hans Konrad Knörr works on Hartree-Fock theory and related approximation methods for quantum mechanical many-body systems, spectral properties of many-particle Schrödinger operators, quantum transport.
- Oliver Matte works on stochastic differential equations for models of matter coupled to quantized radiation fields, spectral analysis of operators in relativistic quantum physics, applications of Fourier integral operators with complex-valued phase functions, semiclassical analysis in large dimension with applications to statistical mechanics, tempered Gibbs measures and associated Dirichlet operators.