The network's overall objective is to develop mathematical tools that allow to treat spectral problems arising in quantum mechanics or other fields of physics using quantum mechanical methods. These mathematical tools - mostly originating from the field of partial differential equations and functional analysis - will be suitable for the description of high-dimensional physical systems. In order to structure the task of actualising the general objective the proposed research has been grouped into four sub-objectives, which are nonetheless closely interrelated:

• to understand selected models of condensed matter from meso- to macroscopic scales
• to understand the stability and dynamics of infinite dimensional quantum systems
• to establish effective models as limits of fundamental equations
• to understand linear and nonlinear aspects of the effective models

Last update: 20 November 2006 aq