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Authors |
B. Khesin G. Misiolek Klas Modin |
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Published in | Proceedings of the National Academy of Sciences of the United States of America |
Volume | 115 |
Issue | 24 |
Pages | 6165-6170 |
ISSN | 0027-8424 |
Publication year | 2018 |
Published at |
Department of Mathematical Sciences |
Pages | 6165-6170 |
Language | en |
Links |
https://doi.org/10.1073/pnas.171934... |
Keywords | hydrodynamics, infinite-dimensional geometry, quantum information, Fisher-Rao, Newton's, quantum-mechanics, optimal transport, equation, fluid, diffeomorphisms, theorem, motion, moser, Science & Technology - Other Topics |
Subject categories | Geometry |
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important partial differential equations of hydrodynamical origin can be described in this framework in a natural way. In particular, the Madelung transform between the Schrodinger equation and Newton's equations is a symplectomorphism of the corresponding phase spaces. Furthermore, the Madelung transform turns out to be a Kahler map when the space of densities is equipped with the Fisher-Rao information metric. We describe several dynamical applications of these results.