Partitioning technique for open systems

Abstract

The focus of the present contribution is essentially confined to three research areas carried out during the author's turns as visiting (assistant, associate and full) professor at the University of Florida's Quantum Theory Project, QTP. The first two topics relate to perturbation theory and spectral theory for self-adjoint operators in Hilbert space. The third subject concerns analytic extensions to non-self-adjoint problems, where particular consequences of the occurrence of continuous energy spectra are measured. In these studies general partitioning methods serve as general cover for perturbation-, variational- and general matrix theory. In addition we follow up associated inferences for the time dependent problem as well as recent results and conclusions of a rather general yet surprising character. Although the author spent most of his times at QTP during visits in the 1970s and 1980s, collaborations with department members and shorter stays continued through later decades. Nevertheless the impact must be somewhat fragmentary, yet it is hoped that the present account is sufficiently self-contained to be realistic and constructive.

Keywords:

• partitioning technique
• time scales
• spectral theory
• complex dilations
• dissipative dynamics
• Jordan blocks
• quantum correlations
• thermal correlations

Acknowledgements

The present research covers periods when the author was an Uppsala visiting (assistant, associate and full) professor at the Quantum Theory Project of the University of Florida. The author is indebted to past and present members as well as the University, in particular the Office of Academic Affairs, for the warm hospitality that was shown to him during these periods. Over the years the US National Science Foundation, the Office of Scientific Research, and the Air Force Office of Scientific Research have supported a large part of the research described here.