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| Authors |
B. Khesin G. Misiolek Klas Modin |
|---|---|
| Published in | Archive for Rational Mechanics and Analysis |
| Volume | 234 |
| Issue | 2 |
| Pages | 549-573 |
| ISSN | 0003-9527 |
| Publication year | 2019 |
| Published at |
Department of Mathematical Sciences |
| Pages | 549-573 |
| Language | en |
| Links |
dx.doi.org/10.1007/s00205-019-01397... |
| Keywords | quantum-mechanics, Mathematics, Mechanics |
| Subject categories | Mathematics |
The Madelung transform is known to relate Schrodinger-type equations in quantum mechanics and the Euler equations for barotropic-type fluids. We prove that, more generally, the Madelung transform is a Kahler map (that is a symplectomorphism and an isometry) between the space of wave functions and the cotangent bundle to the density space equipped with the Fubini-Study metric and the Fisher-Rao information metric, respectively. We also show that Fusca's momentum map property of the Madelung transform is a manifestation of the general approach via reduction for semi-direct product groups. Furthermore, the Hasimoto transform for the binormal equation turns out to be the 1D case of the Madelung transform, while its higher-dimensional version is related to the Willmore energy in binormal flows.
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