An inverse problem from condensed matter physics

Ru Yu Lai; Ravi Shankar; Daniel Spirn; Gunther Uhlmann

doi:10.1088/1361-6420/aa8e81

An inverse problem from condensed matter physics

Ru Yu Lai, Ravi Shankar, Daniel Spirn, Gunther Uhlmann

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by a Hamiltonian system. If the background potential is sufficiently smooth and flat, the background can be reconstructed using ideas from the boundary and the lens rigidity problems. We prove that reconstructions are unique, derive an approximate reconstruction formula, and present numerical examples.

Original language	English (US)
Article number	115011
Journal	Inverse Problems
Volume	33
Issue number	11
DOIs	https://doi.org/10.1088/1361-6420/aa8e81
State	Published - Oct 26 2017

Bibliographical note

Funding Information:
R-YL was partly supported by the AMS-Simons Travel Grants. RS and DS were supported in part by the NSF. GU was partly supported by the NSF, a Si-Yuan Professorship at IAS, HKUST, and a FiDiPro at the University of Helsinki.

Keywords

background potential
inverse problems
uniqueness
vortex dipoles

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abstract = "We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by a Hamiltonian system. If the background potential is sufficiently smooth and flat, the background can be reconstructed using ideas from the boundary and the lens rigidity problems. We prove that reconstructions are unique, derive an approximate reconstruction formula, and present numerical examples.",

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AU - Spirn, Daniel

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N2 - We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by a Hamiltonian system. If the background potential is sufficiently smooth and flat, the background can be reconstructed using ideas from the boundary and the lens rigidity problems. We prove that reconstructions are unique, derive an approximate reconstruction formula, and present numerical examples.

AB - We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by a Hamiltonian system. If the background potential is sufficiently smooth and flat, the background can be reconstructed using ideas from the boundary and the lens rigidity problems. We prove that reconstructions are unique, derive an approximate reconstruction formula, and present numerical examples.

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KW - uniqueness

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