论文标题
关于随机Schrödinger系统的单实现回收率的最新进展
On recent progress of single-realization recoveries of random Schrödinger systems
论文作者
论文摘要
我们考虑通过在单个随机性实现下产生的量子散射中的近场或远场数据来恢复一些统计量。我们调查了文献的最新进展，并指出了现有结果之间的相似性。还研究了正向问题重新制定的方法。我们考虑使用近场和远场数据的两个单独的案例，并讨论获得一些至关重要的渐近估计的关键思想。我们特别关注使用伪差操作员理论和证明中所需的微局部分析。
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.
