Electromagnetic compatibility in complex environments – predicting the propagation of electromagnetic waves using wave-chaos theory

Project description

Electromagnetic systems and devices are often complicated, irregular in their geometry and heterogeneous in their electrical characteristics. Such a system could be a PC, a mobile phone, or even an airplane cockpit. The prediction of the energy distribution becomes hard when using traditional analytical and numerical tools, especially if the wavelength is small compared to the size of the structure. Statistical methods are often more appropriate to describing the physical process under investigation in such cases. Appropriately chosen, such methods can lead to surprisingly simple and physically understandable characterization of the problem, which can be used to exploit complexity and turn collective behaviour into beneficial engineering technology.

This PhD project uses a phase-space representation of wave fields, the so-called Wigner distribution function (WDF), to unveiled transport properties of fields using tools of dynamical system theory. An exact evolution operator for the transport of these Wigner functions can be derived, and approximation schemes are obtained by using ray families that include reflections from irregular boundaries. The project will explore the possibility of linking the WDF operator to existing semiclassical approximations of quantum mechanics, used to transport densities of quantum particles. The challenge lies in constructing a phase space picture of those operators through the WDF before including the source operator.