Sum rules and constraints on passive systems - a general approach and applications to electromagnetic scattering

Sammanfattning: Physical processes are often modeled as input-output systems. Many such systems obey passivity, which means that power is dissipated in the process. This thesis deals with the inevitable constraints imposed on physical systems due to passivity. A general approach to derive sum rules and physical limitations on passive systems is presented. The sum rules relate the dynamical behaviour of a system to its static and/or high-frequency properties. This is beneficial, since static properties are in general easier to determine. The physical limitations indicate what can, and what can not, be expected from certain passive systems. At the core of the general approach is a set of integral identities for Herglotz functions, a function class intimately related to the transfer functions of passive systems. In this thesis, the general approach is also applied to a specific problem: the scattering and absorption of electromagnetic vector spherical waves by various objects. Physical limitations are derived, which limit the absorption of power from each individual spherical wave. They are particularly useful for electrically small scatterers. The results can be used in many fields where an understanding of the interaction between electromagnetic waves and matter is vital. One interesting application is within antenna theory, where the limitations are helpful from a designer's viewpoint; they can give an understanding as to what factors limit performance, and also indicate if there is room for improvement or not.