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We consider the recovery of some statistical quantities by using thenear-field or far-field data in quantum scattering generated under a singlerealization of the randomness. We survey the recent main progress in theliterature and point out the similarity among the existing results. Themethodologies in the reformulation of the forward problems are alsoinvestigated. We consider two separate cases of using the near-field andfar-field data, and discuss the key ideas of obtaining some crucial asymptoticestimates. We pay special attention on the use of the theory ofpseudodifferential operators and microlocal analysis needed in the proofs.

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