A1 Journal article (refereed)
Determining a Random Schrödinger Operator : Both Potential and Source are Random (2021)

Li, J., Liu, H., & Ma, S. (2021). Determining a Random Schrödinger Operator : Both Potential and Source are Random. Communications in Mathematical Physics, 381(2), 527-556. https://doi.org/10.1007/s00220-020-03889-9

JYU authors or editors

Publication details

All authors or editors: Li, Jingzhi; Liu, Hongyu; Ma, Shiqi

Journal or series: Communications in Mathematical Physics

ISSN: 0010-3616

eISSN: 1432-0916

Publication year: 2021

Volume: 381

Issue number: 2

Pages range: 527-556

Publisher: Springer

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s00220-020-03889-9

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/72935

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1906.01240


We study an inverse scattering problem associated with a Schrödinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We then derive two unique recovery results in determining the rough strengths of the random source and the random potential, by using the corresponding far-field data. The first recovery result shows that a single realization of the passive scattering measurements uniquely recovers the rough strength of the random source. The second one shows that, by a single realization of the backscattering data, the rough strength of the random potential can be recovered. The ergodicity is used to establish the single realization recovery. The asymptotic arguments in our study are based on techniques from the theory of pseudodifferential operators and microlocal analysis.

Keywords: partial differential equations; inverse problems; mathematical models; electromagnetic radiation; scattering (physics)

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

Preliminary JUFO rating: 3

Last updated on 2021-07-07 at 17:56