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Causality, sum rules, and scattering bounds

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MWSW02 - Theory of wave scattering in complex and random media

Many physical systems satisfy causality, i.e., the effect cannot precede its cause. In this presentation, we explore some of the consequences of this concept. We use a class of analytic functions that maps the upper complex half plane onto itself. These functions are called Herglotz functions, and they are instrumental in our treatment. We employ a set of integral identities, which gives a collection of sum rules. These sum rules can be applied to scattering and transmission problems and give physical bounds on the system. We exemplify with a series of examples from electromagnetic problems. The acoustic problem is briefly discussed as well as some possible extensions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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