Abstract

In the past two decades a lot of effort has been invested into the spectral analysis of quantum field theoretic models of nonrelativistic matter which is coupled to the quantized radiation field. One of the approaches is the renormalization group based on the (smooth or sharp) Feshbach-Schur map. Ground state and resonance eigenvectors have been constructed by means of this method.

In a joint work with Jacob Schach Mller and Matthias Westrich it is shown that the long-time asymptotics of the dynamics of (some of) these systems can also be iteratively obtained by a similar method called the “Dynamical Renormalization Group”. In particular it is shown that, for a given time scale $t im g^{-n}$ in powers of the coupling constant $g$, an effective Hamiltonian is derived, which generates the dynamics modula small errors. For $n=2$, this effective Hamiltonian coincides with the well-known operator obtained in the van Hove (= weak coupling) limit.