Geometry and Dynamics of Gaussian Wave Packets and their Wigner Transforms
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Ohsawa, Tomoki and Tronci, Cesare (2017) Geometry and Dynamics of Gaussian Wave Packets and their Wigner Transforms Journal of Mathematical Physics, 58 (9). pp. 1-19.
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Geometry and Dynamics of Gaussian Wave Packets and their Wigner Transforms.pdf - Accepted version Manuscript Download (282kB) | Preview |
Abstract
We find a relationship between the dynamics of the Gaussian wave packet and the dynamics of the corresponding Gaussian Wigner function from the Hamiltonian and symplecticgeometric point of view. The main result states that the momentum map corresponding to the natural action of the symplectic group on the Siegel upper half space yields the covariance matrix of the corresponding Gaussian Wigner function. This fact, combined with Kostant’s coadjoint orbit covering theorem, establishes a symplectic/Poisson-geometric connection between the two dynamics.
| Item Type: | Article | |||||||||
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| Divisions : | Faculty of Engineering and Physical Sciences > Mathematics | |||||||||
| Authors : |
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| Date : | 13 August 2017 | |||||||||
| DOI : | 10.1063/1.4995233 | |||||||||
| Copyright Disclaimer : | Reproduced from Ohsawa,Tomoki,Tronci,Cesare.Journal of Mathematical Physics, volume 58, number 9, page no's 092105 1-19,with the permission of AIP Publishing | |||||||||
| Uncontrolled Keywords : | Gaussian wave packet; Wigner function; momentum maps; Hamiltonian dynamics; Lie–Poisson equation; coadjoint orbit; semiclassical mechanics. | |||||||||
| Depositing User : | Jane Hindle | |||||||||
| Date Deposited : | 22 Aug 2017 14:44 | |||||||||
| Last Modified : | 05 Jul 2019 16:13 | |||||||||
| URI: | http://epubs.surrey.ac.uk/id/eprint/841997 |
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