Transfer operator approach for cavities with apertures

We describe a representation of the boundary integral equations for wave propagation in enclosures which leads to a direct description of transport and dynamical characteristics of the problem. The formalism is extended to account for arbitrary and possibly statistical sources driving a polygonal cavity problem and to account for apertures. In this approach, the boundary integral equations are encoded within a shift operator which propagates waves leaving the boundary until they return to the boundary as an incoming wave. The response of the system to non-deterministic, statistical sources characterised by correlation functions can be treated, providing a direct path to ray-tracing approaches through the Wigner function. The high frequency limit is retrieved semiclassically and provides a simple ray tracing scheme transporting densities of rays as an averaged response. Interference effects due to transport along multiple paths can also be accounted for.