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Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states

Tronci, C and Bonet-Luz, E (2016) Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states Proceedings of the Royal Society A, 472 (2189).

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Abstract

The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical operators are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest’s theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie-Poisson structure associated to another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models previously appeared in the chemical physics literature.

Item Type: Article
Subjects : subj_Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Tronci, CUNSPECIFIEDUNSPECIFIED
Bonet-Luz, EUNSPECIFIEDUNSPECIFIED
Date : 11 May 2016
Funders : EPSRC
Identification Number : 10.1098/rspa.2015.0777
Copyright Disclaimer : Copyright © 2016 The Royal Society. All rights reserved.
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 08 Apr 2016 14:25
Last Modified : 18 May 2016 16:18
URI: http://epubs.surrey.ac.uk/id/eprint/810384

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