An inverse problem from condense matter physics
Analysis of PDEs
2017-11-22 v3
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.
Cite
@article{arxiv.1606.07352,
title = {An inverse problem from condense matter physics},
author = {Ru-Yu Lai and Ravi Shankar and Daniel Spirn and Gunther Uhlmann},
journal= {arXiv preprint arXiv:1606.07352},
year = {2017}
}
Comments
30 pages, 7 figures. Two new sections: reconstruction formula and numerical examples