Semiclassical Transfer Operator for Complex Built-up Structures

We investigate the wave energy distribution in complex built-up structures with multiple interfaces at which the material properties change discontinuously. We formulate the transfer operator in such a way that it can in principle be made exact, and it is clear where the semiclassical approximations are made at each stage of the derivation. We reformulate the boundary integral equations for the Helmholtz equation in terms of incoming and outgoing boundary waves independently of the boundary conditions and decomposing the green functions into singular and regular components. For demonstration purposes, we apply a semiclassical form of the operator (corresponding to a high-frequency approximation) to polygonal coupled-cavity configurations with abrupt changes of the material properties (such as wave speed and absorption coefficients at the interfaces between the cavities).