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.

6 pages, 3 figures (published version: layout changed and refs updated)

References in corpus (6)

• Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
• Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption
• Universal statistics of the local Green's function in quantum chaotic systems with absorption
• Microwave fidelity studies by varying antenna coupling
• Fluctuations in an established transmission in the presence of a complex environment
• Fluctuations and correlations in scattering on a resonance coupled to a chaotic background

Cited by in corpus (3)

• Implementing Non-Universal Features with a Random Matrix Theory Approach: Application to Space-to-Configuration Multiplexing
• Statistics of a simple transmission mode on a lossy chaotic background
• Scarring in open chaotic systems: The local density of states