Abstract
This work develops a general approach to quantify fluctuations in scattering on a simple mode coupled to a lossy chaotic background. The paper derives the exact joint distribution of reflection and total transmission at arbitrary absorption and establish a remarkable symmetry between fluctuations in reflection and transmission sectors. The results are further applied to study the statistics of total losses, which is relevant in a broader context of wave chaotic systems.
Highlights
Strength function phenomena [1] have a rich history of various applications in atomic and nuclear physics [2,3,4,5,6] as well as in open mesoscopic systems [7,8,9,10]
Following the random matrix theory (RMT) paradigm [28,29], we model Hbg by a random N × N matrix drawn from the Gaussian orthogonal (GOE) or unitary (GUE) ensemble, depending on the presence or absence of time-reversal invariance (TRI), respectively
The approach developed shows that scattering on the simple mode coupled to the complex background serves as a sensitive probe of its internal structure
Summary
Strength function phenomena [1] have a rich history of various applications in atomic and nuclear physics [2,3,4,5,6] as well as in open mesoscopic systems [7,8,9,10] In such problems, one deals with a “simple” excitation (associated with a specific signal) that is coupled to the background of many “complicated” (usually chaotic) states. For the complete characterization of the scattering process, both transmission and reflection fluctuations need to be treated at the same time This becomes even more challenging at finite losses, since the two are no longer related by the flux conservation. We study marginal densities and the statistics of total losses
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