Envelope and phase distribution of a resonance transmission through a complex environment.
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 any coupling to the background with arbitrary absorption. The intensity and phase are distributed within certain region, revealing essential correlations even at strong absorption. In the latter limit, we obtain a simple asymptotic expression that provides uniformly good approximation of the exact distribution within its whole support, thus going beyond Rician distribution often used for such purposes. Exact results are also derived for the marginal distribution of the phase as well as for its limiting forms at weak and strong absorption.
Publisher URL: http://arxiv.org/abs/1710.11071