On recent progress of single-realization recoveries of random Schr\"odinger systems

TL;DR

This paper reviews recent advances in recovering statistical properties of random Schrödinger systems from single realizations using near-field and far-field data, highlighting key analytical techniques involved.

Contribution

It provides a comprehensive survey of recent progress and emphasizes the role of pseudodifferential operators and microlocal analysis in these recovery methods.

Findings

Summarizes recent progress in single-realization recovery methods.

Highlights the use of pseudodifferential operators and microlocal analysis.

Discusses asymptotic estimates for near-field and far-field data.

Abstract

We consider the recovery of some statistical quantities by using the near-field or far-field data in quantum scattering generated under a single realization of the randomness. We survey the recent main progress in the literature and point out the similarity among the existing results. The methodologies in the reformulation of the forward problems are also investigated. We consider two separate cases of using the near-field and far-field data, and discuss the key ideas of obtaining some crucial asymptotic estimates. We pay special attention on the use of the theory of pseudodifferential operators and microlocal analysis needed in the proofs.