Envelope and phase distribution of a resonance transmission through a complex environment

Abstract

A transmission amplitude is considered for quantum or wave transport mediated by a single resonance coupled to the background of many chaotic states. Such a model provides a useful approach to quantify fluctuations in an established signal induced by a complex environment. Applying random matrix theory to the problem, we derive an exact result for the joint distribution of the transmission intensity (envelope) and the transmission phase at arbitrary coupling to the background with finite absorption. The intensity and phase are distributed within a certain region, revealing essential correlations even at strong absorption. In the latter limit, we obtain a simple asymptotic expression that provides a uniformly good approximation of the exact distribution within its whole support, thus going beyond the Rician distribution often used for such purposes. Exact results are also derived for the marginal distribution of the phase, including its limiting forms at weak and strong absorption.

Implementing Non-Universal Features with a Random Matrix Theory Approach: Application to Space-to-Configuration Multiplexing

“…Such exceptions imply that simply using centered quantities S ij − S ij does not always guarantee Rayleigh statistics in a tunablemetasurface-stirred chaotic cavity. Indeed, it was recently shown that in the presence of a deterministic scattering component the transmission amplitude and phase develop nontrivial statistical correlations even at strong absorption [50]. Such correlations may also impact techniques using such centered quantities, for instance, for antenna characterization in reverberation chambers [51].…”

Scarring in open chaotic systems: The local density of states

“…Scattering is of fundamental importance to understand, for example, transport properties in mesoscopic systems [31,32], ionization or photoabsorption in complex atoms and molecules [33,34], the effects of absorption in devices such as microwave cavities [35][36][37] or microwave networks [38][39][40], and directed radiation from dielectric optical microcavities [41][42][43][44] with an underlying chaotic classical dynamics. It is then natural to investigate dynamical properties and wave function statistics of open chaotic systems to address both fundamental and practical questions, such as understanding deviations from the RMT results due to absorption [45][46][47][48][49][50][51][52][53][54][55], or how scars are modified by the opening [56][57][58][59]. Regarding the latter issue, scarring is often assessed by visual inspection of realand phase-space (e.g., Husimi or Wigner) distributions, or by counting statistics of the wave function intensities.…”