An inverse problem from condensed matter physics

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

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish (US)
Article number115011
JournalInverse Problems
Issue number11
StatePublished - 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.

Publisher Copyright:
© 2017 IOP Publishing Ltd.


  • background potential
  • inverse problems
  • uniqueness
  • vortex dipoles


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