Page Manager: Webmaster
Last update: 9/11/2012 3:13 PM
| Authors |
B. Khesin G. Misiolek Klas Modin |
|---|---|
| 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.
© UNIVERSITY OF GOTHENBURG • Sweden • Box 100 • SE-405 30 Gothenburg
Phone: +46 31 786 0000 • Contact • Organisation number: 202100-3153
About the website
Facebook
Twitter
Instagram
Youtube
Weibo