American Institute of Mathematical Sciences

doi: 10.3934/era.2020121

On recent progress of single-realization recoveries of random Schrödinger systems

 Department of Mathematics and Statistics, University of Jyväskylä, Finland

Received  May 2020 Revised  October 2020 Published  November 2020

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.

Citation: Shiqi Ma. On recent progress of single-realization recoveries of random Schrödinger systems. Electronic Research Archive, doi: 10.3934/era.2020121
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