Work

An inverse problem from condensed matter physics

Year: 2017

Type: article

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.

Source: Inverse Problems

DOI: 10.1088/1361-6420/aa8e81

Authors: Ru-Yu Lai, Ravi Shankar, Daniel Spirn, Gunther Uhlmann

Institutions: University of Minnesota, University of Washington, University of Helsinki, Hong Kong University of Science and Technology

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

OpenAlex ID: W2471066251

FWCI: 0.91

Cites: 37

Cited by: 6

Related to: