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Geometry and Dynamics of Gaussian Wave Packets and their Wigner Transforms

Ohsawa, Tomoki and Tronci, Cesare (2017) Geometry and Dynamics of Gaussian Wave Packets and their Wigner Transforms Journal of Mathematical Physics.

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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
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Ohsawa, TomokiUNSPECIFIEDUNSPECIFIED
Tronci, Cesarec.tronci@surrey.ac.ukUNSPECIFIED
Date : 2017
Copyright Disclaimer : Reproduced from Ohsawa,Tomoki,Tronci,Cesare.Journal of Mathematical Physics, 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 : 22 Aug 2017 14:44
URI: http://epubs.surrey.ac.uk/id/eprint/841997

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