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Momentum maps for mixed states in quantum and classical mechanics

Tronci, Cesare (2019) Momentum maps for mixed states in quantum and classical mechanics Journal of Geometric Mechanics.

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Abstract

This paper presents the momentum map structures which emerge in the dynamics of mixed states. Both quantum and classical mechanics are shown to possess analogous momentum map pairs associated to left and right group actions. In the quantum setting, the right leg of the pair identifies the Berry curvature, while its left leg is shown to lead to different realizations of the density operator, which are of interest in quantum molecular dynamics. Finally, the paper shows how alternative representations of both the density matrix and the classical density are equivariant momentum maps generating new Clebsch representations for both quantum and classical dynamics. Uhlmann’s density matrix and Koopman wavefunctions are shown to be special cases of this construction.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Tronci, Cesarec.tronci@surrey.ac.uk
Date : 2019
Funders : Leverhulme Trust, London Mathematical Society
Copyright Disclaimer : © American Institute of Mathematical Sciences 2019.
Related URLs :
Additional Information : For Darryl Holm, on the occasion of his 70th birthday.
Depositing User : Clive Harris
Date Deposited : 25 Jul 2019 15:14
Last Modified : 25 Jul 2019 15:14
URI: http://epubs.surrey.ac.uk/id/eprint/852309

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