Determining a Random Schrödinger Operator : Both Potential and Source are Random
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
Julkaistu sarjassa
Communications in Mathematical PhysicsPäivämäärä
2021Tekijänoikeudet
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
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.
Julkaisija
SpringerISSN Hae Julkaisufoorumista
0010-3616Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/47084905
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Lisätietoja rahoituksesta
The work of J. Li was partially supported by the NSF of China under the Grant Nos. 11571161 and 11731006, the Shenzhen Sci-Tech Fund No. JCYJ20170818153840322. The work of H. Liu was partially supported by Hong Kong RGC general research funds, Nos. 12302017, 12301218, 12302919 and 12301420.Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities
Lu, Shuai; Salo, Mikko; Xu, Boxi (IOP Publishing, 2022)We consider increasing stability in the inverse Schrödinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential ... -
Spherically Symmetric Terrestrial Planets with Discontinuities Are Spectrally Rigid
Ilmavirta, Joonas; de Hoop, Maarten V.; Katsnelson, Vitaly (Springer, 2024)We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two ... -
The higher order fractional Calderón problem for linear local operators : Uniqueness
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse; Uhlmann, Gunther (Elsevier, 2022)We study an inverse problem for the fractional Schrödinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the one of the fractional Laplacian. We show that ... -
Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse (American Institute of Mathematical Sciences (AIMS), 2021)We prove a unique continuation property for the fractional Laplacian (−Δ)s when s∈(−n/2,∞)∖Z where n≥1. In addition, we study Poincaré-type inequalities for the operator (−Δ)s when s≥0. We apply the results to show that ... -
Optimality of Increasing Stability for an Inverse Boundary Value Problem
Kow, Pu-Zhao; Uhlmann, Gunther; Wang, Jenn-Nan (Society for Industrial & Applied Mathematics (SIAM), 2021)In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for the Schrödinger equation. The rigorous justification of increasing stability for the IBVP for the Schrödinger ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.