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

Physical Review. E
Dmitry V Savin

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.

References

May 21, 2005·Physical Review Letters·U KuhlH-J Stöckmann
Oct 10, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sameer HemmadySteven M Anlage
Jun 4, 2008·Physical Review Letters·S AbergA Richter
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B DietzH A Weidenmüller
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B KöberT H Seligman
Mar 10, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jen-Hao YehSteven M Anlage
Aug 6, 2013·Physical Review Letters·S KumarF Schäfer
Jan 20, 2018·Physical Review. E·Dmitry V SavinFabrice Mortessagne

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