On the theory of cavities with point-like perturbations: part I. General theory

Abstract

Abstract. The theoretical interpretation of measurements of "wavefunctions" and spectra in electromagnetic cavities excited by antennas is considered. Assuming that the characteristic wavelength of the field inside the cavity is much larger than the radius of the antenna, we describe antennas as "pointlike perturbations". This approach strongly simplifies the problem reducing the whole information on the antenna to four effective constants. In the framework of this approach we overcame the divergency of series of the phenomenological scattering theory and justify assumptions lying at the heart of "wavefunction measurements". This selfconsistent approach allowed us to go beyond the one-pole approximation, in particular, to treat the experiments with degenerated states. The central idea of the approach is to introduce "renormalized" Green function, which contains the information on boundary reflections and has no singularity inside the cavity. PACS numbers:On the theory of cavities with point-like perturbations. Part I: General theory 2

Disordered graphene and boron nitride in a microwave tight-binding analog

“…A detailed derivation of the renormalized Green function can be found in Ref. 47. It is not clear how the coupling parameter Λ(E, R) depends on E or even on the LDoS.…”

“…With the methods developed in Ref. 47, it is possible to derive an approximative description of the coupling for small cylindrical antennas showing an almost frequency independent prefactor Λ(E, R). Hence we finally obtain the relation between the LDoS and the reflection that is given by…”

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“…In Ref. 35 it was shown that for the correct analysis of transport one has to take into account the influence of coupling between the antennas and the waveguide. As a result, the Green's function for the empty waveguide in the normal-mode representation reads…”

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