An inverse problem from condensed matter physics

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http://hdl.handle.net/10138/307555

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Lai , R-Y , Shankar , R , Spirn , D & Uhlmann , G 2017 , ' An inverse problem from condensed matter physics ' , Inverse Problems , vol. 33 , no. 11 , 115011 . https://doi.org/10.1088/1361-6420/aa8e81

Title: An inverse problem from condensed matter physics
Author: Lai, Ru-Yu; Shankar, Ravi; Spirn, Daniel; Uhlmann, Gunther
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2017-11
Language: eng
Number of pages: 32
Belongs to series: Inverse Problems
ISSN: 0266-5611
URI: http://hdl.handle.net/10138/307555
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.
Subject: vortex dipoles
background potential
uniqueness
inverse problems
LANDAU-SCHRODINGER EQUATION
BOSE-EINSTEIN CONDENSATE
VORTEX DYNAMICS
ANDERSON LOCALIZATION
QUANTIZED VORTICES
SUPERFLUID HE-4
MOTION
STABILITY
GEODESICS
RIGIDITY
111 Mathematics
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