A2 Review article, Literature review, Systematic review
On recent progress of single-realization recoveries of random Schrödinger systems (2021)

Ma, S. (2021). On recent progress of single-realization recoveries of random Schrödinger systems. Electronic Research Archive, 29(3), 2391-2415. https://doi.org/10.3934/era.2020121

JYU authors or editors

Publication details

All authors or editors: Ma, Shiqi

Journal or series: Electronic Research Archive

eISSN: 2688-1594

Publication year: 2021

Volume: 29

Issue number: 3

Pages range: 2391-2415

Publisher: American Institute of Mathematical Sciences (AIMS)

Publication country: United States

Publication language: English

DOI: https://doi.org/10.3934/era.2020121

Publication open access: Openly available

Publication channel open access: Open Access channel

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2005.10670

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.

Keywords: inverse problems; partial differential equations; potential theory; quantum mechanics; scattering (physics); mathematical models

Free keywords: inverse scattering; random source and medium; ergodicity; pseudodifferential operators; microlocal analysis.

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 1